Kinetic Theory of Gases MCQ Quiz in বাংলা - Objective Question with Answer for Kinetic Theory of Gases - বিনামূল্যে ডাউনলোড করুন [PDF]

Ans. (c)

Sol. Kinetic gas equation, PV = \(\frac{1}{3} \mathrm{mN}_{\mathrm{a}} \mathrm{u}^2\)

\(P V=\frac{1}{3} mN_a u^2 \times \frac{2}{2}=\frac{2}{3} N_a \times \frac{1}{2} \mathrm{mu}^2=\frac{2}{3} N_a E\)

\(\mathrm{P}=\frac{2}{3 V} \overline{\mathrm{E}} \mathrm{N}_{\mathrm{a}}\)

Ans. (b)

Sol. \(\lambda=\frac{1}{\sqrt{2} n d^2}=\frac{1}{\sqrt{2} \times 1 \times 10^{-20}}=\frac{10^{20}}{\sqrt{2}}\)

≈ 10¹⁹

Ans. (a)

Sol. According to kinetic theory, the gas particles have same mass but negligible volume compared to the volume of the gas.

Ans. (a)

Sol. 

\(\left(u_{a v}\right)_{H_2}=\sqrt{\frac{8 R T}{\pi M_{H_2}}} \text { and }\left(u_{a v}\right)_{D_2}=\sqrt{\frac{8 R T}{\pi M_{D_2}}}\)

\(\frac{\left(u_{a v}\right)_{H_2}}{\left(u_{a v}\right)_{D_2}}=\frac{M_{H_2}}{M_{D_2}}=\sqrt{\frac{2}{4}}=\frac{1}{\sqrt{2}}\)

\(\left(u_{a v}\right)_{D_2}=\frac{1.78}{1.41}\)

= 1.26 km sec^-1

Ans. (d)

Sol. V_rms of a gas = 30 R^1/2

\(\mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}}=30 R^{1 / 2} \Leftrightarrow \sqrt{\frac{3 \times 300}{M}}=30\)

\(\frac{\sqrt{900}}{30}=\sqrt{M}\)

M = 1 g mol^-1 = 10^-3 kg mol^-1

Ans. (a)

Sol. Van der waal’s constant ′a′ is a measure of inter molecular forces and ′b′ is a measure of molecular size.

So, in comparison to C₂H₂, both the van der waal’s constants for He will be smaller.

Ans. (a)

Sol.

 \(\begin{array}{cc} \mathrm{V}=8.2 \mathrm{~L} \quad \mathrm{P} & =380 \text { torr } \quad \mathrm{T}=300 \mathrm{~K} \\ & =\frac{380}{760}=0.5 \mathrm{~atm} \end{array}\)

PV = nRT

\(\mathrm{n}=\frac{P V}{R T}=\frac{0.5 \times 8.2}{0.0821 \times 300}\) = 0.1664 moles

Number of molecules = n × N_a

= 0.1664 × 6.023 × 10²³ molecules

= 1.002 × 10²³ molecules

Rate of effusion, r ∝ \(\rm \sqrt{{\frac{1}{M}}}\) ( where M is molar mass )

Thus we have,

\(\rm \frac{r(N_2)}{r(CO_2)}=\sqrt{\frac{M(CO_2)}{M(N_2)}}=\sqrt{\frac{44}{28}}=\sqrt{\frac{11}{7}}\)

Mean free path, 

\(\rm λ=\frac{RT}{\sqrt2\pi d^2NP}\)

So, λ ∝ T/P