NCERT Exemplar Class 11 Chemistry Chapter 5: Higher Order Thinking Skills (HOTS) Questions
Class 11 States of Matter Questions and Answers are given below that will help students to solve complex problems. These solutions will help you evaluate your understanding of the concepts.
Question 1. How many times does the pressure of an ideal gas inside a cubic of side l change if the side is reduced to 1/2 and the temperature is kept constant?
(i) 1.9
(ii) 1.8
(iii) 2.4
(iv) 3.6
Answer:
$
\mathrm{P}=\frac{1}{3} \frac{\mathrm{mNu}^2}{\mathrm{v}}=\frac{2}{3 \mathrm{v}}\left(\frac{1}{2} \mathrm{mNu}^2\right)=\frac{2}{3 \mathrm{v}}(\mathrm{kE})
$
Temperature is constant, hence ( KE ) remains instant.
Volume initially of side $(I)=1^3$
Volume due to the change to $\left(\frac{1}{2}\right)^3=\frac{1^3}{8}$
Thus,
$
\mathrm{P}_1=\frac{2}{3} \frac{\mathrm{kE}}{\mathrm{l}^2}, \mathrm{P}_2=\frac{2}{3} \frac{\mathrm{kE}}{\mathrm{l}^3} \times \delta
$
therefore, $\frac{\mathrm{P}_2}{\mathrm{P}_1}=8$
Hence, the answer is option (ii).
Question 2: The diffusion coefficient of an ideal is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 8 times, and its pressure 4 times. As a result, the diffusion coefficient of this gas increases A time. The value of A is -
(i) 1.4
(ii) 2.2
(iii) 3.8
(iv) 4.10
Answer:
Rate of diffusion $\alpha \lambda \propto \mathrm{U}_{\mathrm{Avg}}$
$
\begin{aligned}
& \alpha \frac{1}{\sqrt{2} \pi \sigma^2 \mathrm{~N}^*} \times \mathrm{U}_{\mathrm{Avg}} \\
& \alpha \frac{1}{\sqrt{2} \pi \sigma^2 \mathrm{~N}^*} \\
& \alpha \frac{\mathrm{U}_{\mathrm{Avg}}(\mathrm{KT})}{\sqrt{2} \mathrm{n} \sigma^2 \mathrm{P}}
\end{aligned}
$
Rate of diffuaion $\alpha \frac{\mathrm{T}^{3 / 2}}{\mathrm{p}}$
$
\frac{r_{\text {final }}}{r_{\text {inital }}}=\frac{(8)^{3 / 2}}{(4)}=2
$
Hence, the correct answer is option (ii).
Question 3. 0.4g of dihydrogen is made to react with 7.1g of dichlorine to form hydrogen chloride. Calculate the volume of hydrogen chloride formed at 273K and 1 bar pressure?
Answer:
The reaction occurs as follows:
$\mathrm{H}_2+\mathrm{Cl}_2 \rightarrow 2 \mathrm{HCl}$
Now, clearly 2g of hydrogen reacts with 71g of chlorine.
Thus, 0.4g of hydrogen will react with 14.2g of chlorine.
Thus, no reactant is the limiting reagent here. Both the reactants will consume completely.
Thus, 2g of hydrogen will produce 73g of HCl.
Thus, 0.4g of hydrogen will produce 14.6g of HCl.
Now, moles of HCl produced = 7.3/73 = 0.2 moles
Now, according to the ideal gas equation, we have:
PV = nRT
Thus, V = (nRT)/P
V = (0.2 x 0.0821 x 273)/1
V = 4.54L
Hence, the answer is 4.54 L.
Question 4: An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density $1000 \mathrm{~kg} / \mathrm{m}^3$. If the pressure inside the bubble is $2100 \mathrm{~N} / \mathrm{m}^2$ greater than the atmosphet ic pressure, then the surface tension of the liquid m . SI unit is (use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )
(1) 0.02
(2) 0.1
(3) 0.25
(4) 0.05
Answer:
$P_{\text {bubble }}=P_{\text {atm }}+\rho g h+\frac{2 S}{r}$
Given
Given that the pressure inside the bubble is $P_{\text {atm }}+2100 \mathrm{~N} / \mathrm{m}^2$
The liquid pressure at a depth of 20 cm is
$
P_{\text {liquid }}=P_{\mathrm{atm}}+\rho g h=P_{\mathrm{atm}}+1000 \times 10 \times 0.20=P_{\mathrm{atm}}+2000 \mathrm{~N} / \mathrm{m}^2,
$
the pressure difference due solely to surface tension is
$
\Delta P=\left(P_{\text {bombubble }}-P_{\text {liquid }}\right)=\left(P_{\text {atm }}+2100\right)-\left(P_{\text {atm }}+2000\right)=100 \mathrm{~N} / \mathrm{m}
$
The Laplace pressure difference for a bubble (which has one interface) is given by $\Delta P=\frac{2 S}{r}$.
The given bubble radius is 0.1 cm , which in SI units is
$
r=0.1 \mathrm{~cm}=0.001 \mathrm{~m} .
$
Substituting the known values into the Laplace equation gives
$
\frac{2 S}{0.001}=100
$
Solving for $S$ :
$
\begin{aligned}
& 2 S=100 \times 0.001=0.1 \\
& S=\frac{0.1}{2}=0.05 \mathrm{~N} / \mathrm{m}
\end{aligned}
$
Hence, the correct answer is option (4).
Question 5: The purification method based on the following physical transformation is :
$\underset{(\mathrm{X})}{\mathrm{Solid}} \xrightarrow{\text { Heat }} \underset{(\mathrm{X})}{\text { Vapour }} \xrightarrow{\text { Cool }} \underset{(\mathrm{X})}{\text { Solid }}$
(1) Sublimation
(2) Distillation
(3) Crystallization
(4) Extraction
Answer:
$\underset{(X)}{\text { Solid }} \xrightarrow{\text { Heat }} \underset{(X)}{\text { Vapour }} \xrightarrow{\text { Cool }} \underset{(X)}{\text { Solid }}$
is known as Sublimation.
In sublimation, a solid substance directly transforms into its gaseous phase upon heating and reverts back to the solid phase upon cooling. This technique is commonly used to purify substances, particularly those that sublime more easily than others under the same conditions. Sublimation is effective for separating substances with different volatility, like separating ammonium chloride from a mixture with sodium chloride, as ammonium chloride sublimates while sodium chloride does not.
Hence, the correct answer is option (1).
Question 6: At a given temperature T , gases $\mathrm{Ne}, \mathrm{Ar}, \mathrm{Xe}$ and kr are found to deviate from ideal gas behaviour
$\mathrm{P}=\frac{\mathrm{RT}}{\mathrm{~V}-\mathrm{b}} \text { al } \mathrm{T}$
This equation of state is given as, $\mathrm{P}=\frac{\mathrm{R}}{\mathrm{V}-\mathrm{b}}$ al T . Which gas will exhibit steepest increase in the plot of ?
(1) $\mathrm{X}{\mathrm{e}}$
(2) Ar
(3) Kr
(4) Ne
Answer:
Noble gases such as Ne ,Ar ,Xe ,Kr found to deviate from ideal gas behaviour.
Xe gas will exhibit stepest increase in plot of 2 vsP.
$\begin{aligned} P=\frac{R T}{(V-b)} \Rightarrow & P(V-b)=R T \\ \Rightarrow & P V-P b=R T \\ \Rightarrow & \frac{P V}{R T}=1+\frac{P b}{R T} \\ \Rightarrow & z=\frac{P V}{R T} \\ & =1+\frac{\mathrm{Pb}}{\mathrm{RT}} \Rightarrow \mathrm{y}=\mathrm{c}+\mathrm{mx}\end{aligned}$
Hence the answer is the option (1).
Question 7: The density of a gas A is thrice that of a gas B at the same temperature .The molecular weight of gas B is twice that of A.What will the ratio of the pressure acting on A and B is _____
(1) $\frac{1}{4}$
(2) $\frac{7}{8}$
(3) $\frac{2}{5}$
(4) $\frac{1}{6}$
Answer:
$\frac{\mathrm{d}}{\mathrm{P}}=\frac{\mathrm{M}}{\mathrm{RT}}$
Let the density of gas B be d
of gas A =3d
and the molecular weight of A be M and the molecular of B will be 2 M,
Since,
R is gas constant and T is the same for both gases, so ____
$\begin{aligned} & P_A=\frac{d_A R T}{M_A} \therefore \frac{P_B}{P_A}=\frac{d_B}{d_A} \times \frac{M_A}{M_B}=\frac{d}{3 d} \times \frac{M}{2 M} \\ & P_B=\frac{d_B R T}{M_B}=\frac{1}{6}\end{aligned}$
Hence, the answer is the option (4).
NCERT Exemplar Class 11 Chemistry Chapter 5: Important Formulas
Given below are Class 11 Chemistry chapter 5 States of matter important formulas that are essential for solving numerical problems. Go through these formulas carefully.
1. Gas Laws:
Boyle's law: Pressure–Volume relation at constant T.
$P\propto \frac{1}{V}$ or PV = Constant
Charle's law: Volume–Temperature relation at constant P.
$V\propto T$ or $\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}$
Gay-Lussac's law: Pressure–Temperature relation at constant V.
$P\propto T$ or $\frac{P_{1}}{T_{1}}=\frac{P_{2}}{T_{2}}$
Avogadro's law:
$V\propto n$ or $\frac{V_{1}}{n_{1}}=\frac{V_{2}}{n_{2}}$
2. Ideal Gas Equation:
PV = nRT
Where:
3. Density and Molar Mass
$d(density)=\frac{PM}{RT} $ , Where M = Molar Mass
4. Mole Fraction
$x_{i}=\frac{n_{i}}{n_{total}}$ and $p_{i}=x_{i}P_{total}$
5. Average Kinetic Energy of Gas Molecules
Average $KE=\frac{3}{2}RT$ (per mole)
6. Root Mean Square Speed ( rms speed)
$u_{rms}=\sqrt{\frac{3RT}{M}}$ , (M should be in kg/mol)
7. Real Gas - Van der Waals equation
$(P+\frac{an^{2}}{V^{2}})(V-nb)=nRT$
Where, a measures of intermolecular attraction and b measures of finite molecular volume.
8. Compressibility Factor (Z)
$Z=\frac{PV}{nRT}$ ,
-
For ideal gases: Z=1
-
For real gases: Z≠1