NCERT Solutions for Class 11 Chemistry Chapter 7 Equilibrium

Question 7.1(a) A liquid is in equilibrium with its vapour in a sealed container at a fixed temperature. The volume of the container is suddenly increased.

What is the initial effect of the change on vapour pressure?

Answer :

By increasing the volume of the container suddenly, initially, the vapour pressure would decrease. It is due to, the amount of vapour has remained the same but it is distributed in a larger volume.

Question 7.1(b) A liquid is in equilibrium with its vapour in a sealed container at a fixed temperature. The volume of the container is suddenly increased.

How do rates of evaporation and condensation change initially?

Answer :

Here the temperature is constant so that the rate of evaporation is also the same as before. On increasing the volume of the container, the density of vapour decreases due to which the rate of collision between vapour particles decreases. Hence the condensation rate also decreases initially.

Question 7.1(c) A liquid is in equilibrium with its vapour in a sealed container at a fixed temperature. The volume of the container is suddenly increased .

What happens when equilibrium is restored finally and what will be the final vapour pressure?

Answer :

When equilibrium is restored, the rate of evaporation is equal to the rate of condensation. The temperature is constant and the volume is changed. The vapour pressure is temperature-dependent, not volumes. So, that final vapour pressure is equal to the initial vapour pressure.

Question 7.2 What is K _c for the following equilibrium when the equilibrium concentration of each substance is: [SO ₂ ]= 0.60M, [O ₂ ] = 0.82M and [SO ₃ ] = 1.90M ?

Answer :

Followings are the given information values to solve the above problems-

The given chemical equation is -

The equilibrium constant for this reaction is expressed as;


(approx)

Question 7.3 At a certain temperature and total pressure of 10 ⁵ Pa, iodine vapour contains 40% by volume of I atoms

Calculate Kp for the equilibrium.

Answer :

It is given that total pressure (P _T )is and partial pressure of atom = 40 % of P _T
So, the partial pressure of atom = Pascal

The partial pressure of = 60% of P _T

So, the partial pressure of = Pascal

Now, for the reaction

Question 7.4 Write the expression for the equilibrium constant, K _c for each of the following reactions:

(i)

(ii)

(iii)

(iv)

(v)

Answer :

The equilibrium constant for any reaction can be written as (concentration of products) / (concentration of reactants). And we considered constant values for the solids and liquids because their density per unit volume or mass per unit volume does not change.
Thus,
(i)
(ii)

(iii)

(iv)

(v)

Question 7.5 Find out the value of K _c for each of the following equilibria from the value of K _p :

(i)

(ii)

Answer :

We know that the relation between and is expressed as;

............................(i)
here = (no. of moles of product) - (no. of moles of reactants)

R = 0.0831 bar L /mol/K, and

For (i)
= and Temp (T) = 500K

= 3 - 2 = 1
By putting the all values in eq (i) we get

For (ii)
= and temp(T) = 1073 K
= 2 - 1 = 1
Now, by putting all values in eq (i) we get,

Question 7.6 For the following equilibrium, K _c = 6.3 × 10 ¹⁴ at 1000 K

Both the forward and reverse reactions in the equilibrium are elementary bimolecular reactions. What is K _c , for the reverse reaction?

Answer :

It is given that,

we know that for the reverse reaction is the inverse of the forward equilibrium constant. Thus it can be calculated as:

Question 7.7 Explain why pure liquids and solids can be ignored while writing the equilibrium constant expression?

Answer :

For the pure liquids and solids, the molecular mass and the density at a particular temperature is always fixed and it is considered as a constant. Thus they can be ignored while writing the equilibrium constant expression

Question 7.8 Reaction between N ₂ and O _2- takes place as follows:

If a mixture of 0.482 mol N ₂ and 0.933 mol of O ₂ is placed in a 10 L reaction vessel and allowed to form N ₂ O at a temperature for which K _c = 2.0 ×10 ^-37 , determine the composition of equilibrium mixture.

Answer :

It is given that,

Let the concentration of at equilibrium be . So,

initial conc 0.482 0.933 0 (in moles)
at equilibrium 0.482- 0.933 - (in moles)

The equilibrium constant is very small. So, we can assume 0.482- = 0.482 and 0.933 - = 0.933

We know that,

{dividing the moles by 10 to get concentration of ions)

So, the concentration of

Question 7.9 Nitric oxide reacts with Br ₂ and gives nitrosyl bromide as per reaction given below:

When 0.087 mol of NO and 0.0437 mol of Br ₂ are mixed in a closed container at a constant temperature, 0.0518 mol of NOBr is obtained at equilibrium. Calculate the equilibrium amount of NO and Br ₂ .

Answer :

The initial concentration of and is 0.087 mol and 0.0437 mol resp.

The given chemical reaction is-

Here, 2 mol of produces from 2 mol of . So, 0.0518 mol of is obtained from 0.518 mol of .

Again, From 1 mol of two mol of produced. So, to produce 0.518 mol of we need mol of .

Thus, the amount of present at equilibrium = 0.087 - 0.0518 = 0.0352 mol

and the amount of present at the equilibrium = 0.0437-0.0259 = 0.0178 mol

Question 7.10 At 450K, K _p = 2.0 × 10 ¹⁰ /bar for the given reaction at equilibrium.

What is K _c at this temperature?

Answer :

We have,

We know that the relation between and ;

Here = ( moles of product) - (moles of reactants)

So. here = 2-3 = -1

By applying the formula we get;

= 7.48

Question 7.11 A sample of HI(g) is placed in flask at a pressure of 0.2 atm. At equilibrium the partial pressure of HI(g) is 0.04 atm. What is K _p for the given equilibrium?

Answer :

The initial pressure of is 0.2 atm . At equilibrium, it has a partial pressure of 0.04 atm. Therefore, a decrease in the pressure of is 0.2 - 0.04 = 0.16 .

The given reaction is:

At equilibrium,

Therefore,

Question 7.12 A mixture of 1.57 mol of N ₂ , 1.92 mol of H ₂ and 8.13 mol of NH ₃ is introduced into a 20 L reaction vessel at 500 K. At this temperature, the equilibrium constant, K _c for the reaction is 1.7 × 10 ² . Is the reaction mixture at equilibrium? If not, what is the direction of the net reaction?

Answer :

We have,

The concentration of species are-

We know the formula of

The reaction is not in equilibrium. Since , the equilibrium proceeds in reverse direction.

Question 7.13 The equilibrium constant expression for a gas reaction is,

Write the balanced chemical equation corresponding to this expression.

Answer :

The balanced chemical equation corresponding to the given expression can be written as:

Question 7.14 One mole of H ₂ O and one mole of CO are taken in 10 L vessel and heated to 725 K. At equilibrium 40% of water (by mass) reacts with CO according to the equation,

Calculate the equilibrium constant for the reaction.

Answer :

The given reaction is-

initial conc 1/10 1/10 0 0
At equilibrium 0.6/10 0.6/10 0.04 0.04

Now, the equilibrium constant for the reaction can be calculated as;

= 0.44 (approx)

Question 7.15 At 700 K, equilibrium constant for the reaction:

is 54.8. If 0.5 mol L ^-1 of HI(g) is present at equilibrium at 700 K, what are the concentration of H ₂ (g) and I ₂ (g) assuming that we initially started with HI(g) and allowed it to reach equilibrium at 700K?

Answer :

We have,

The equilibrium constant of the reaction =

moles of = 0.5 mol/L

The given reaction is-

So, the reverse equilibrium constant is

Suppose the concentration of hydrogen and iodine at equilibrium be

Therefore,

So, the value of =

Question 7.16 What is the equilibrium concentration of each of the substances in the equilibrium when the initial concentration of ICl was 0.78 M ?

Answer :

The given reaction is:

Initial conc. 0.78 M 0 0
At equilibrium (0.78 - 2 ) M M M

The value of

Now we can write,

By solving this we can get the value of = 0.167

Question 7.17 K _p = 0.04 atm at 899 K for the equilibrium shown below. What is the equilibrium concentration of C ₂ H ₆ when it is placed in a flask at 4.0 atm pressure and allowed to come to equilibrium?

Answer :

Suppose the pressure exerted by the hydrogen and ethene gas be at equilibrium.

the given reaction is-

initial pressure 4 atm 0 0
At equilibrium 4 -

Now,

By solving the quadratic equation we can get the value of = 0.38

Hence,at equilibrium,

= 4 - p = 4 -.038

= 3.62 atm

Question 7.18(i) Ethyl acetate is formed by the reaction between ethanol and acetic acid and the equilibrium is represented as:

(i) Write the concentration ratio (reaction quotient), Q _c , for this reaction (note: water is not in excess and is not a solvent in this reactio n)

Answer :

The given reaction is-
the concentration ratio (reaction quotient) of the given chemical reaction is-

Question 7.18(ii) Ethyl acetate is formed by the reaction between ethanol and acetic acid and the equilibrium is represented as:

(ii) At 293 K, if one starts with 1.00 mol of acetic acid and 0.18 mol of ethanol, there is 0.171 mol of ethyl acetate in the final equilibrium mixture. Calculate the equilibrium constant.

Answer :

Let the volume of the mixture will be V.

initial conc. 1/V 0.18/V 0 0

At equilibrium (= 0.829/V)

So the equilibrium constant for the reaction can be calculated as;

(approx)

Question 7.18(iii) Ethyl acetate is formed by the reaction between ethanol and acetic acid and the equilibrium is represented as:

(iii) Starting with 0.5 mol of ethanol and 1.0 mol of acetic acid and maintaining it at 293 K, 0.214 mol of ethyl acetate is found after sometime. Has equilibrium been reached?

Answer :

Let the volume of the mixture will be V.

initial conc. 1/V 0.5/V 0 0

At equilibrium (= 0.786/V)

Therefore the reaction quotient of the reaction-

Since equilibrium has not been reached.

Question 7.19 A sample of pure PCl ₅ was introduced into an evacuated vessel at 473 K. After equilibrium was attained, concentration of PCl ₅ was found to be 0.5 × 10 ^-1 mol L ^-1 . If value of K _c is 8.3 × 10 ^-3 , what are the concentrations of PCl ₃ and Cl ₂ at equilibrium?

Answer :

We have,

concentration of = 0.05 mol/L
and

Suppose the concentrations of both and at equilibrium be mol/L. The given reaction is:

at equilibrium 0.05

it is given that the value of the equilibrium constant,

Now we can write the expression for equilibrium as:

(approx)

Hence the concentration of and is 0.0204 mol / L

Question 7.20 One of the reaction that takes place in producing steel from iron ore is the reduction of iron(II) oxide by carbon monoxide to give iron metal and CO ₂ . ; K _p = 0.265 atm at 1050K What are the equilibrium partial pressures of CO and CO ₂ at 1050 K if the initial partial pressures are: = 1.4 atm and = 0.80 atm?

Answer :

We have,

the initial pressure of and are 1.4 atm and 0.80atm resp.

The given reaction is-

initially, 1.4 atm 0.80 atm

Since the reaction will proceed in the backward direction to attain equilibrium. The partial pressure of will increase = decrease in the partial pressure of =

By solving the above equation we get the value of = 0.339 atm

Question 7.21 Equilibrium constant, K _c for the reaction

At 500 K is 0.061 At a particular time, the analysis shows that composition of the reaction mixture is 3.0 mol L ^-1 N ₂ , 2.0 mol L ^-1 H ₂ and 0.5 mol L ^-1 NH ₃ . Is the reaction at equilibrium? If not in which direction does the reaction tend to proceed to reach equilibrium?

Answer :

The given reaction is:

at a particular time: 3.0molL ^-1 2.0 molL ^-1 0.5molL ^-1

Now, we know that,

It is given that K _c = 0.061

Since, Qc Kc, the reaction mixture is not at equilibrium.

Again, , the reaction will proceed in the forward direction to attain the equilibrium.

Question 7.22 Bromine monochloride, BrCl decomposes into bromine and chlorine and reaches the equilibrium:

For which K _c = 32 at 500 K. If initially pure BrCl is present at a concentration of 3.3 × 10 ^-3 mol L ^-1 , what is its molar concentration in the mixture at equilibrium?

Answer :

Suppose the amount of bromine and chlorine formed at equilibrium. The given reaction is:

Initial Conc. 0 0

at equilibrium - 2

Now, we can write,

By solving the above equation we get,

=

Hence, at equilibrium
M

Question 7.23 At 1127 K and 1 atm pressure, a gaseous mixture of CO and CO ₂ in equilibrium with soild carbon has 90.55% CO by mass

Calculate K _c for this reaction at the above temperature .

Answer :

Suppose the total mass of the gaseous mixture is 100 g.
Total pressure is 1 atm

Mass of = 90.55 g
And, mass of = (100 - 90.55) = 9.45 g

Now, number of moles of = 90.55/28 = 3.234 mol (mol. wt of = 28)
Number of moles of = 9.45/44 = 0.215 mol (mol. wt of = 44)

Partial pressure of ,

= 0.938 atm

Similarly partial pressure of ,

= 0.062 atm

Thus,

By using the relation

= 0.159 (approx)

Question 7.24 Calculate a) for the formation of NO2 from NO and O2 at 298K

where

Answer :

Given data,

given chemical reaction-

for the reaction,
= (products) - (reactants)
= (52-87-0)
= -35 kJ/mol

Question 7.25 Does the number of moles of reaction products increase, decrease or remain same when each of the following equilibria is subjected to a decrease in pressure by increasing the volume?

(a)

(b)

(c)

Answer :

According to Le Chatellier's principle, if the pressure is decreased, then the equilibrium will shift in the direction in which more number of moles of gases is present.

So,

• (a)The number of moles of reaction products will increase.
• (b)The number of moles of reaction products will decrease
• (c)The number of moles of reaction products remains the same.

Question 7.26 Which of the following reactions will get affected by increasing the pressure? Also, mention whether the change will cause the reaction to go into forward or backward direction.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Answer :

According to Le Chatellier's principle , if the pressure is increased, then the equilibrium will shift in the direction in which less number of moles of gases is present. So, as per this rule following given reactions are affected by the increasing pressure-

The reaction (i), (iii), and (vi)- all proceeds in the backward direction

Reaction(iv) will shift in the forward direction because the number of moles of gaseous reactants is more than that of products.

Question 7.27 The equilibrium constant for the following reaction is 1.6 ×10 ⁵ at 1024K

Find the equilibrium pressure of all gases if 10.0 bar of HBr is introduced into a sealed container at 1024K .

Answer :

Given that,
for the reaction =

Let the pressure of both and at equilibrium be .

initial conc. 10 0 0
at eq 10-2p p p

Now,



By solving the above equation we get,

= 0.00248 bar

Hence the pressure of and is 0.00248 bar and pressure of is 0.00496 bar

Question 7.28(a) Dihydrogen gas is obtained from natural gas by partial oxidation with steam as per following endothermic reaction:

Write an expression for Kp for the above reaction.

Answer :

the expression of ionisation constant ( Kp) for the reaction can be defined as the ratio of the product of concentration to the product of reactants.

Question 7.28(b) Dihydrogen gas is obtained from natural gas by partial oxidation with steam as per following endothermic reaction:

How will the values of Kp and composition of equilibrium mixture be affected by

(i) increasing the pressure

(ii) increasing the temperature

(iii) using a catalyst?

Answer :

(i) According to Le Chatellier's principle, if pressure is increased, then the reaction will shift towards the less number of moles of gases. So, here the direction of equilibrium is backward and the value of decreases.

(ii) According to Le Chatellier's principle, as the reaction is endothermic, the equilibrium will shift in the forward direction. The value of is increases.

(iii) The equilibrium of the reaction is not affected by the presence of the catalyst. It only increases the rate of reaction.

Question 7.29(a) Describe the effect of :

(a) addition of H ₂

Answer :

(a)According to Le Chatelliers principle, on the addition of dihydrogen, the number of mole of increases on the reactant side. Thus to attain the equilibrium again the reaction will move in the forward direction.

(b) According to Le Chatellier's principle, on the addition of methyl alcohol, the number of moles of methyl alcohol increases on the product sides. So, to attain the equilibrium, the reaction will proceed in a backward direction.

(c) If we remove the from the reactant side, the concentration on the reactant side will decrease and to attain an equilibrium, the reaction will shift backward direction

(d) On removal of the equilibrium will shift in the forward direction.

Question 7.29(b) Describe the effect of :

addition of CH ₃ OH

Answer :

According to Le Chatellier's principle, on the addition of methyl alcohol, the number of moles of methyl alcohol increases on the product sides. So, to attain the equilibrium, the reaction will proceed in a backward direction.

Question 7.29(c) Describe the effect of :

removal of CO

Answer :

If we remove the from the reactant side, the concentration on the reactant side will decrease and to attain an equilibrium, the reaction will shift backward direction

Question 7.30 At 473 K, equilibrium constant K _c for decomposition of phosphorus pentachloride, PCl ₅ is 8.3 ×10 ^-3 . If decomposition is depicted as,

(a) write an expression for Kc for the reaction.
(b) what is the value of K _c for the reverse reaction at the same temperature ?
(c) what would be the effect on K _c if

(i) more PCl ₅ is added
(ii) pressure is increased
(iii) the temperature is increased ?

Answer :

We have,

Equilibrium constant for the above reaction =

(a) Expression of for this reaction-

(b) The value of reverse equilibrium constant can be calculated as;

(c).i would remain the same because the temperature is constant in this case.

(c). ii If we increase the pressure, there is no change in because the temperature is constant in this case also.

(c). iii In an endothermic reaction, the value of increases with increase in temperature.

Question 7.31 Dihydrogen gas used in Haber’s process is produced by reacting methane from natural gas with high temperature steam. The first stage of two stage reaction involves the formation of CO and H ₂ . In second stage, CO formed in first stage is reacted with more steam in water gas shift reaction,

If a reaction vessel at 400 °C is charged with an equimolar mixture of CO and steam such that = 4.0 bar, what will be the partial pressure of H ₂ at equilibrium? Kp= 10.1 at 400°C

Answer :

We have,
The partial pressure of and is 4 bar and the
Let be the partial pressure of and at equilibrium. The given reaction is-


Initial concentration 4 bar 4 bar 0 0
At equilibrium 4 - 4 -

Therefore, we can write,


By solving the above equation we get, = 3.04

Hence, the partial pressure of dihydrogen at equilibrium is 3.04 bar

Question 7.32 Predict which of the following reaction will have an appreciable concentration of reactants and products:

(a)
(b)
(c)

Answer :

If the value of is in the range of to , then the reaction has appreciable concentrations of both reactants and products.

Therefore, the third reaction (c) will have an appreciable concentration of reactants and products.

Question 7.33 The value of K _c for the reaction is 2.0 ×10 ^-50 at 25°C. If the equilibrium concentration of O ₂ in air at 25°C is 1.6 ×10 ^-2 , what is the concentration of O ₃ ?

Answer :

We have,

equilibrium constant of the reaction =
the concentration of dioxygen =

the given reaction is-

Then we have,
(equilibrium constant)

Thus the concentration of dioxygen is

Question 7.34(a) The reaction,

is at equilibrium at 1300 K in a 1L flask. It also contain 0.30 mol of , 0.10 mol of and 0.02 mol of and an unknown amount of CH ₄ in the flask. Determine the concentration of CH ₄ in the mixture. The equilibrium constant, K _c for the reaction at the given temperature is 3.90.

Answer :

Given that,
Total volume = 1L
0.3 mol of , 0.10 mol of dihydrogen( )and the 0.02 mol of water( )
the equilibrium constant = 3.90

Let be the concentration of methane at equilibrium. The given reaction is-

At equilibrium, 0.3 mol/L 0.1 mol/L 0.02 mol/L

Therefore,

Thus the concentration of methane at equilibrium is

Question 7.34(b) What is meant by the conjugate acid-base pair? Find the conjugate acid/base for the following species:

Answer :

A conjugate acid-base pair means that the species are differed by only one proton. for example; is an acid because it donates a proton to water. So , and these pairs are called conjugate acid-base pair.

Species	Conjugate acid-base
	(Base)
	(Acid)
	(base)
	(acid)
	(acid)
	(acid)
	(acid)

Question 7.35 Which of the followings are Lewis acids?

Answer :

Lewis acid-
Those species which can accept the pair of electrons are called Lewis acids. For example Boron trifluoride ( ), ammonium ion( ) and the hydrogen ion( ). Among them water molecule is a Lewis base, it can donate pair of electrons.

Question 7.36 What will be the conjugate bases for the Brönsted acids: ?

Answer :

When Brönsted acids lose their proton then they become a conjugate base of that corresponding acids.
Followings are the conjugate base of Brönsted acid-

Question 7.38 Write the conjugate acids for the following Brönsted bases: .

Answer :

When Brönsted base accepts a proton then they become a conjugate acid of that corresponding base.
Followings are the conjugate acid of Brönsted base-

Question 7.39 The species: can act both as Brönsted acids and bases. For each case give the corresponding conjugate acid and base.

Answer :

When acid or base accept or lose a proton, they form conjugate acid or base of that corresponding species.

Lists of the conjugate acid and conjugate base of the given species-

Species	Conjugate acid	Conjugate base

Question 7.40 Classify the following species into Lewis acids and Lewis bases and show how these act as Lewis acid/base:
(a)
(b)
(c) .
(d)

Answer :

Species which donate pair of an electron are called Lewis base and which accepts pair of electrons are called acid.

(a) is a Lewis base since it can donate its lone pair of electrons.

(b) is a Lewis base since it can donate a pair of electrons.

(c) is a Lewis acid since it can accept a pair of electrons.

(d) is a Lewis acid since it can accept a pair of electrons.

Question 7.41 The concentration of hydrogen ion in a sample of soft drink is 3.8 × 10 ^-3 M. what is its pH?

Answer :

We have,
the concentration of Hydrogen ion sample is M
So,

Question 7.42 The pH of a sample of vinegar is 3.76. Calculate the concentration of hydrogen ion in it.

Answer :

We have,
The pH of a sample of vinegar is 3.76
=?

Therefore,

Taking antilog on both sides we get,
= antilog (-3.76)

Hence the concentration of hydrogen ion

Question 7.43 The ionization constant of HF, HCOOH and HCN at 298K are 6.8 × 10 ^-4 , 1.8 × 10 ^-4 and 4.8 × 10 ^-9 respectively. Calculate the ionization constants of the corresponding conjugate base.

Answer :

We have,
IOnization constant of hydrogen fluoride, methanoic acid and hydrogen cyanide are and respectively.

It is known that,
...........................(i)

of the conjugate base

Similarly,
By using the equation (i)
of the conjugate base

Again, with the help of eq (i)
of the conjugate base

Question 7.44 The ionization constant of phenol is 1.0 × 10 ^-10 . What is the concentration of phenolate ion in 0.05 M solution of phenol? What will be its degree of ionization if the solution is also 0.01M in sodium phenolate?

Answer :

We have,
The ionization constant of phenol is , and
the concentration of phenol is 0.05 M
degree of ionisation = ?

Ionization of phenol;

At equilibrium,
the concentration of various species are-


As we see, the value of ionisation is very less. Also will be very small. Thus we can ignore .

Hence the concentration of phenolate ion is

Let be the degree of dissociation of phenol in the presence of 0.01 M of phenolate ion.

Concentration (1 - ) 0.05 0.05 0.05

So,

therefore,

The degree of dissociation is

Question 7.45 The first ionization constant of H ₂ S is 9.1 × 10 ^-8 . Calculate the concentration of HS ^- ion in its 0.1M solution. How will this concentration be affected if the solution is 0.1M in HCl also? If the second dissociation constant of H2S is 1.2 × 10 ^-13 , calculate the concentration of S ^2- under both conditions.

Answer :

We have,
1st ionisation constant of hydrogen sulphide is and the 2nd dissociation constant is

Case 1st-(absence of hydrochloric acid)

To calculate the concentration of
Let be the concentration of and the ionisation of hydrogen sulphide is;

0.1 M

At equilibrium, the concentration of various species are,
Since the dissociation constant is is very small. So, can be neglected.
the concentration of = 1- M
the concentration of and is M
So,

from here can be calculated and we get,

Case 2nd (In presence of 0.1 M, HCl)
Suppose is dissociated is .Then at equilibrium,
and the
So,

Thus the concentration of [ ] is

Question 7.46 The ionization constant of acetic acid is 1.74 × 10 ^-5 . Calculate the degree of dissociation of acetic acid in its 0.05 M solution. Calculate the concentration of acetate ion in the solution and its pH.

Answer :

It is given,
The ionisation constant of acetic acid is and concentration is 0.05 M

The ionisation of acetic acid is;

Therefore,

So, the of the solution =
=
=

We know that,

Question 7.47 It has been found that the pH of a 0.01M solution of an organic acid is 4.15. Calculate the concentration of the anion, the ionization constant of the acid and its pK _a .

Answer :

We have,
pH of organic acid is 4.15 and its concentration is 0.01M

Suppose the organic acid be HA. The dissociation of organic acid can be written as;

(By taking antilog of -4.15)

Now,

[HA] = 0.01

Then,

Thus

Question 7.48 Assuming complete dissociation, calculate the pH of the following solutions:

(a) 0.003 M HCl

(b) 0.005 M NaOH

(c) 0.002 M HBr

(d) 0.002 M KOH

Answer :

Assuming the complete dissociation. So,

(a) The ionisation of hydrochloric acid is

Since it is fully ionised then
Therefore,
of the solution =
=
= 2.52

(b) The ionisation of


Therefore,
of the solution =

of the solution is equal to (14 - 2.301 =11.70)

(c) The ionisation of


Therefore,
of the solution =

of the solution is equal to (2.69)

(d) The ionisation of


Therefore,
of the solution =

of the solution is equal to (14 - 2.69 = 11.31)

Question 7.49(a) Calculate the pH of the following solutions:

2 g of TlOH dissolved in water to give 2 litre of solution.

Answer :

Here, 2 g of dissolves in water to give 2 litres of solution
So, the concentration of =
(the molar mass of is 221)

can be dissociated as

Therefore, (since K _{w = )}

So, the concentration of =

Thus
= 11.65(approx)

Question 7.49(b) Calculate the pH of the following solutions:

0.3 g of dissolved in water to give 500 mL of solution.

Answer :

The calcium hydroxide ion dissociates into-

Molecular weight of = 74
the concentration of =

We know that,

=

Thus
= 14 - 1.79 = 12.21

Question 7.49(c) Calculate the pH of the following solutions:

0.3 g of NaOH dissolved in water to give 200 mL of solution.

Answer :

dissociates into
So, the concentration of =

We know that ,

Now, =

Question 7.49(d) Calculate the pH of the following solutions:

1mL of 13.6 M HCl is diluted with water to give 1 litre of solution.

Answer :

We know that,
M ₁ V ₁ (before dilution) = M ₂ V ₂ (after dilution)

initially V _{1 =} 1mL and M ₁ = 13.6 M
and V ₂ = 1L and M ₂ = ?

By putting all these values we get,

Thus
= 1.86 (approx)

Question 7.50 The degree of ionization of a 0.1M bromoacetic acid solution is 0.132. Calculate the pH of the solution and the pK _a of bromoacetic acid.

Answer :

We have,

Degree of ionization(a) = 0.132
Concentration of bromoacetic acid (C) = 0.1 M

Thus the concentration of
= 0.0132

Therefore

= 1.879

Now, we know that,

So,
(approx)

Question 7.51 The pH of 0.005M codeine solution is 9.95. Calculate its ionization constant and pK _b.

Answer :

We have,
C = 0.005 M
= 9.95 and = 14 - 9.95 = 4.05

we know that

By taking antilog on both sides we get.

concentration of =

C.a =
So, a =

We know that,

Thus

Question 7.52 What is the pH of 0.001M aniline solution? Calculate the degree of ionization of aniline in the solution. Also, calculate the ionization constant of the conjugate acid of aniline.(K _b = )

Answer :

We have,
C = 0.001 M
=
Degree of inozation of aniline (a) = ?
Ionization constant of the conjugate acid ( ) = ?

We know that
=
= (0.001)
Thus
=

Then [Base] = C.a = ( )( )
=

Now,

= 14 - 6.187
= 7.813

It is known that,

So,
This is ionization constant.

Question 7.53(a) Calculate the degree of ionization of 0.05M acetic acid if its pK _a value is 4.74. How is the degree of dissociation affected when its solution also contains

0.01M

Answer :

We have,
C = 0.05 M

By taking antilog on both sides we get,

from here we get the value of

After adding hydrochloric acid, the concentration of ions increases and due to that the equilibrium shifts towards the backward direction. It means dissociation will decrease.

(i) when 0.01 HCl is taken

Initial conc. 0.05 0 0
after dissociation 0.05 - 0.001+

As the dissociation is very small.
So we can write 0.001+ 0.001 and 0.05 - 0.05

Now,

So, the value of =

Now degree of dissociation = (amount dissociated) (amount taken)

=
=

Question 7.53(b) Calculate the degree of ionization of 0.05M acetic acid if its pK _a value is 4.74. How is the degree of dissociation affected when its solution also contains

0.1M in HCl ?

Answer :

Let the amount of acetic acid is dissociated in this case

Initial conc. 0.05 0 0
after dissociation 0.05 - 0.1+

As the dissociation is very small.
So we can write 0.1+ 0.1 and 0.05 - 0.05

So, the value of =

Now the degree of dissociation = (amount dissociated) (amount is taken)

=
=

Question 7.54 The ionization constant of dimethylamine is 5.4 × 10 ^-4 . Calculate its degree of ionization in its 0.02M solution. What percentage of dimethylamine is ionized if the solution is also 0.1M in NaOH?

Answer :

We have,

(Degree of ionization)
Concentration of dimethylamine = 0.02 M

If we add 0.1 M of sodium hydroxide. It is a strong base so, it goes complete ionization

(0.1 M) (0.1 M)

and also,

0.02-

(since the dissociation is very small)

Therefore,

Hence in the presece of 0.1 M of sodium hydroxide , 0.54% of dimethylamine get dissociated.

Question 7.55(a) Calculate the hydrogen ion concentration in the following biological fluids whose pH are given below:

Human muscle-fluid, 6.83

Answer :

We have 6.83

It is known that

Therefore,

By taking antilog on both sides we get,

Question 7.55(b) Calculate the hydrogen ion concentration in the following biological fluids whose pH are given below:

Human stomach fluid, 1.2

Answer :

We have 1.2

It is known that

Therefore,

By taking antilog on both sides we get,

Question 7.55(c) Calculate the hydrogen ion concentration in the following biological fluids whose pH are given below:

Human blood, 7.38

Answer :

we have 7.38

It is known that

Therefore,

By taking antilog on both sides we get,

Question 7.55(d) Calculate the hydrogen ion concentration in the following biological fluids whose pH are given below:

Human saliva, 6.4.

Answer :

we have 6.4

It is known that

Therefore,

By taking antilog on both sides we get,

Question 7.56 The pH of milk, black coffee, tomato juice, lemon juice and egg white are 6.8, 5.0, 4.2, 2.2 and 7.8 respectively. Calculate corresponding hydrogen ion concentration in each

Answer :

We already know that can be calculated as-
to calculate the concentration of = antilog (- )

Thus, the hydrogen ion concentration of followings values are-

(i) of milk = 6.8
Since,
6.8 =
= -6.8

= anitlog(-6.8)

=

(ii) of black coffee = 5.0

Since,

5.0 =

= -5.0

= anitlog(-5.0)

=

(iii) of tomato juice = 4.2

Since,

4.2 =

= -4.2

= anitlog(-4.2)

=

(iv) of lemon juice = 2.2

Since,

2.2 =

= -2.2

= anitlog(-2.2)

=

(v) of egg white = 7.8

Since,

7.8 =

= -7.8

= anitlog(-7.8)

=

Question 7.57 If 0.561 g of KOH is dissolved in water to give 200 mL of solution at 298 K. Calculate the concentrations of potassium, hydrogen and hydroxyl ions.What is its pH?

Answer :

We have 0.562 g of potassium hydroxide ( ). On dissolving in water gives 200 mL of solution.
Therefore, concentration of =

= 2.805 g/L

It is a strong base. So, that it goes complete dissociation.

It is known that,

Therefore,

Question 7.58 The solubility of at 298 K is 19.23 g/L of solution. Calculate the concentrations of strontium and hydroxyl ions and the pH of the solution.

Answer :

By given abova data, we know the solubility of at 298 K = 19.23 g/L

So, concentration of

= (Molecular weight of = 121.63 u)

= 0.1581 M

and the concentration of
Now

It is known that,

=

Therefore

Question 7.59 The ionization constant of propanoic acid is . Calculate the degree of ionization of the acid in its 0.05M solution and also its pH. What will be its degree of ionization if the solution is 0.01M in HCl also?

Answer :

Let the degree of ionization of propanoic acid be . Then Let suppose we can write propanoic acid to be HA,

It is known that,

We have
ionization constant of propanoic acid ( )= and the concentration is 0.005 M

By putting the values in above formula we get,

[Acid] = = C. =

Therefore,

If we add 0.01M hydrochloric acid then,

initial con C 0 0
at equi. C - C 0.01 +

Now, by using the formula of

The value of is calculated as ;
(Degree of ionisation)

Question 7.60 The pH of 0.1M solution of cyanic acid (HCNO) is 2.34. Calculate the ionization constant of the acid and its degree of ionization in the solution.

Answer :

We have,
Concentration of cyanic acid = 0.1 M

Therefore, the concentration of = antilog (-2.34)
=

It is known that,
=

Then Ionization constant ( ) =

Question 7.61 The ionization constant of nitrous acid is 4.5 × 10 ^-4 . Calculate the pH of 0.04 M sodium nitrite solution and also its degree of hydrolysis.

Answer :

We have,
Ionization constant of nitrous acid =
Concentration of sodium nitrite ( ) = 0.04 M
Degree of hydrolysis can be calculated as;

Sodium nitrite is a salt of sodium hydroxide (strong base) and the weak acid ( )

Suppose moles of salt undergoes hydrolysis, then the concentration of-

, and

Therefore

from here we can calculate the value of ;

Now

Therefore the degree of hydrolysis

Question 7.62 A 0.02M solution of pyridinium hydrochloride has pH = 3.44. Calculate the ionization constant of pyridine.

Answer :

Given,
= 3.44

We know that

By taking antilog on both sides we get,
= antilog (- 3.44)

pyridinium hydrochloride completely ionised.

Then = (conc. of products)/ (conc, of reactants)
= (? Concentration is 0.02M)

Now,

(approx)

Question 7.63 Predict if the solutions of the following salts are neutral, acidic or basic:

Answer :

Salts of strong acid and strong base are neutral in nature for example-

Salts of a strong base and weak acid are basic in nature for example-

Salts of strong acid and a weak base are acidic in nature for example-

Question 7.64 The ionization constant of chloroacetic acid is 1.35 × 10 ^-3 . What will be the pH of 0.1M acid and its 0.1M sodium salt solution?

Answer :

We have,
Ionisation constant of chloroacetic acid( ) is
The concentration of acid = 0.1 M
Ionisation if acid, =

We know that,
....................(i)
As it completely ionised

Putting the values in eq (i)


Therefore, of the solution =
=
=

Now,

0.1 M (sod. chloroacetate) is basic due to hydrolysis-

For a salt of strong base+strong acid

Question 7.65 Ionic product of water at 310 K is 2.7 × 10 ^-14 . What is the pH of neutral water at this temperature?

Answer :

We have the ionic product of water at 310 K is
It is known that,
ionic product

SInce , therefore

at 310 K is

here we can calculate the value of concentration.

Thus,

Hence the of neutral water is 6.78

Question 7.66(a) Calculate the pH of the resultant mixtures:

10 mL of 0.2M Ca(OH) ₂ + 25 mL of 0.1M HCl

Answer :

Given that,
Vol. of 0.2 M = 10 mL
Vol. of 0.1 M HCl = 25 mL

therefore, by using the formula,


By substituting the value in these equations, we get;

Now,

since

= 14-1.221
= 12.78

Question 7.66(b) Calculate the pH of the resultant mixtures:

10 mL of 0.01M H ₂ SO ₄ + 10 mL of 0.01M Ca(OH) ₂

Answer :

In this case, both the solutions have the same number of moles of and , therefore they both can get completely neutralised. Hence the = 7.0

Question 7.66(c) Calculate the pH of the resultant mixtures:

c) 10 mL of 0.1M H ₂ SO ₄ + 10 mL of 0.1M KOH

Answer :

Given that,

Volume of 0.1 M = 10 mL, and

Volume of 0.1 M = 10 mL

So, by using the formula of,

By putting the values we get,

Hence,

Question 7.67 Determine the solubilities of silver chromate, barium chromate, ferric hydroxide, lead chloride and mercurous iodide at 298K from their solubility product constants given in Table. Determine also the molarities of individual ions.

Answer :

Solubility product is the product of ionic concentrations in a saturated solution.

(i) silver chromate ( )
Ionization of silver chromate

Let " " be the solubility of


According to the table of =

(ii) Barium chromate ( )
Ionization of silver chromate

Let " " be the solubility of


According to the table of =

(iii) Ferric hydroxide ( )
Ionization of Ferric hydroxide

Let " " be the solubility of


According to the table of =

(iv)

Lead chloride ( )
Ionization of Lead chloride

Let " " be the solubility of


According to the table of =

So molarity of and molarity of

Question 7.68 The solubility product constant of Ag ₂ CrO ₄ and AgBr is 1.1 × 10 ^-12 and 5.0 × 10 ^-13 respectively. Calculate the ratio of the molarities of their saturated solutions.

Answer :

silver chromate ( )
Ionization of silver chromate

Let " " be the solubility of


of =

Ionization of Silver bromide ( )

of =

Now, the ratio of solubilities

Question 7.69 Equal volumes of 0.002 M solutions of sodium iodate and cupric chlorate are mixed together. Will it lead to precipitation of copper iodate? (For cupric iodate K _sp = 7.4 × 10 ^-8 ).

Answer :

We have,
solubility product ( ) of cupric iodate =

When equal volumes of sodium iodate and cupric chlorate are mixed together the molar concentration of both the solution becomes half (= 0.001)

Ionization of cupric iodate is;

0.001 M 0.001 M

So, can be calculated as;

Sinc eionic product is less than the so no precipitation occurs.

Question 7.70 The ionization constant of benzoic acid is 6.46 × 10 ^-5 and Ksp for silver benzoate is 2.5 × 10 ^-13 . How many times is silver benzoate more soluble in a buffer of pH 3.19 compared to its solubility in pure water?

Answer :

It is given that,
of buffer solution is 3.19. So, the concentration of ion can be calculated as;

= antilog (-3.19)
=

Ionization of benzoic acid;

It is given that
Therefore,

Question 7.71 What is the maximum concentration of equimolar solutions of ferrous sulphate and sodium sulphide so that when mixed in equal volumes, there is no precipitation of iron sulphide? (For iron sulphide, K _sp = 6.3 × 10 ^-18 ).

Answer :

We have,
The solubility product of the

Equals number of moles of ferrous sulphate and sodium sulphide are mixed in an equal volume.

Let be the concentration of ferrous sulphate and sodium sulphide. On mixing the equimolar solution, the volume of the concentration becomes half.
So,

The ionisation of ferrous sulphide;

Therefore, for no precipitation, ionic product = solubility product

By solving the above equation, we get


The maximum concentration of both the solution is M

Question 7.72 What is the minimum volume of water required to dissolve 1g of calcium sulphate at 298 K? (For calcium sulphate, K _sp is 9.1 × 10 ^-6 )

Answer :

We have,
The solubility product of calcium sulphate is .
given mass of calcium sulphate = 1g

Ionization of calcium sulphate;

Therefore,

Let the solubility of calcium sulphate be .
Then,

mol/L

Thus,
mass/ (mol. wt) volume Molarity
mass =

So, that to dissolve 1 g of calcium sulphate we need = of water.

Question 7.73 The concentration of sulphide ion in 0.1M HCl solution saturated with hydrogen sulphide is 1.0 × 10 ^-19 M. If 10 mL of this is added to 5 mL of 0.04 M solution of the following: in which of these solutions precipitation will take place?

Answer :

We have,
the concentration of and the volume of the solution containing sulphur ion = 10 mL.
Volume of metal salts solution added = 5mL
Before mixing,

M

After mixing,

Volume = 15 mL

So, the concentration of

concentration of

So, the ionic product =
=
=

For the precipitation of the solution, the ionic product should be greater than the corresponding values.
of are and respectively.

Hence precipitation will take place in and metal salts.