Kinetic Theory of Gases NEET प्रश्न हिंदी में — भौतिक विज्ञान (Physics) MCQ उत्तर सहित

$$\begin{gathered} \left(\mathrm{B}\right). \mathrm{For} \mathrm{ideal} \mathrm{gases}. \\ \mathrm{PV}=\mathrm{nRT}=\frac{\mathrm{m}}{\mathrm{M}} \mathrm{RT}:\mathrm{P}=\frac{\mathrm{RT}}{\mathrm{M}}\left(\frac{\mathrm{m}}{\mathrm{V}}\right)=\frac{\mathrm{RT}}{\mathrm{M}} \mathrm{d} \\ \left(\mathrm{or}\right) \mathrm{M}=\mathrm{RT}\left(\frac{\mathrm{d}}{\mathrm{P}}\right). \\ \mathrm{Given} : \mathrm{d}=2.00 \mathrm{P}+0.020 {\mathrm{P}}^2\left(\mathrm{for} \mathrm{a} \mathrm{real} \mathrm{gas}\right). \\ \frac{\mathrm{d}}{\mathrm{P}}=2.00+0.040 \mathrm{P} : \underset{\mathrm{P}\to 0}{\mathrm{Lt}}\frac{\mathrm{d}}{\mathrm{P}}=2.00, \\ \mathrm{which} \mathrm{is} \frac{\mathrm{d}}{\mathrm{P}} \mathrm{for} \mathrm{an} \mathrm{ideal} \mathrm{gas}. \\ \mathrm{Thus} \mathrm{M}=\mathrm{RT} \mathrm{x} 2=25 \mathrm{x} 2=50 \mathrm{g} {\mathrm{Mol}}^{-1}. \end{gathered}$$

$$\begin{gathered} \left(\mathrm{C}\right). \mathrm{Mass} \mathrm{of} \mathrm{water} \mathrm{filled} \mathrm{in} \mathrm{the} \mathrm{glass} \mathrm{vessel}, \\ {\mathrm{m}}_1=\left(148.0-50.0\right)\mathrm{g} =98.0 \mathrm{g} \\ \mathrm{Volume} \mathrm{of} \mathrm{glass} \mathrm{vessel}, \\ \mathrm{V}=\frac{{\mathrm{m}}_1}{\mathrm{\rho }}=\frac{98.0 \mathrm{g}}{0.98 \mathrm{g} {\mathrm{mol}}^{-1}}= 100 \mathrm{mL} = 0.1 {\mathrm{dm}}^3 \\ \mathrm{Mass} \mathrm{of} \mathrm{gas} \mathrm{filled} \mathrm{in} \mathrm{the} \mathrm{vessel}, \mathrm{m} = \left(50.5 – 50.0\right)\mathrm{g} = 0.5 \mathrm{g} \\ \mathrm{If} \mathrm{M} \mathrm{is} \mathrm{the} \mathrm{molar} \mathrm{mass} \mathrm{of} \mathrm{the} \mathrm{gas}, \mathrm{we} \mathrm{will} \mathrm{have} \\ \mathrm{pV}=\mathrm{nRT}=\frac{\mathrm{m}}{\mathrm{M}}\mathrm{RT} \\ \mathrm{or} \mathrm{M}=\frac{\mathrm{mRT}}{\mathrm{pV}} \\ =\frac{\left(0.5\mathrm{g}\right)\left(8.314 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}\right)\left(300 \mathrm{K}\right)}{\left(101.325 \mathrm{kPa}\right)\left(0.1 {\mathrm{dm}}^3\right)}=123 \mathrm{g} {\mathrm{mol}}^{-1} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{A}\right). \mathrm{We} \mathrm{have} {\mathrm{u}}_{\mathrm{av}}=\sqrt{\frac{8\mathrm{RT}}{\mathrm{\pi M}}} \\ \mathrm{Hence}, \sqrt{\frac{8{\mathrm{RT}}_1}{\mathrm{\pi M}}}=9.0\times {10}^4 \mathrm{cm} {\mathrm{s}}^{-1} \\ \mathrm{or} {\mathrm{T}}_1={\left(9.0\times {10}^2 \mathrm{m} {\mathrm{s}}^{-1}\right)}^2\left(\frac{\mathrm{\pi M}}{8\mathrm{R}}\right)={\left(9.0\times {10}^2 \mathrm{m} {\mathrm{s}}^{-1}\right)}^2 \\ \left[\frac{\left(3.14\right)\left(44\times {10}^{-3} \mathrm{kg} {\mathrm{mol}}^{-1}\right)}{\left(8\right)\left(8.314 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}\right)}\right]=1682.5 \mathrm{K} \\ \mathrm{For} \mathrm{most} \mathrm{probable} \mathrm{speed}, \mathrm{we} \mathrm{have} \\ \sqrt{\frac{3{\mathrm{RT}}_2}{\mathrm{M}}}=9.0\times {10}^2 \mathrm{m} {\mathrm{s}}^{-1} \\ \mathrm{Hence}, {\mathrm{T}}_2={\left(9.0\times {10}^2 \mathrm{m} {\mathrm{s}}^{-1}\right)}^2\left(\frac{\mathrm{M}}{2\mathrm{R}}\right) \\ ={\left(9.0\times {10}^2 \mathrm{m} {\mathrm{s}}^{-1}\right)}^2\left[\frac{44\times {10}^{-3} \mathrm{kg} {\mathrm{mol}}^{-1}}{\left(2\right)\left(8.314 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}\right)}\right]=2143.4 \mathrm{K} \end{gathered}$$

4.

माना Ne का द्रव्यमान x तथा Ar का द्रव्यमान y है

x + y = 30  ...(i)

Ar का मोलर द्रव्यमान = 40 g

Ne का मोलर द्रव्यमान = 20 g

नियॉन के मोल + आर्गन के मोल = कुल मोल

$$\begin{gathered} \frac{\mathrm{x}}{20} + \frac{\mathrm{y}}{40} = \mathrm{n} \\ \mathrm{Total} \mathrm{of} \mathrm{K}.\mathrm{E}. = \frac{3}{2}\mathrm{nRT} \\ \mathrm{Given}, \\ \mathrm{K}.\mathrm{E}. = 3 \mathrm{KJ}, \mathrm{T} = 250 \mathrm{K}, \mathrm{R} = 8.314 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1} \\ 3000 \mathrm{J} = \frac{3}{2}\left(\frac{\mathrm{x}}{20} + \frac{\mathrm{y}}{40}\right) \times 8.314 \times 250 \\ 2\mathrm{x} + \mathrm{y} = 38.48 ...\left(\mathrm{ii}\right) \\ \mathrm{From} \left(\mathrm{i}\right) \mathrm{and} \left(\mathrm{ii}\right) \\ \mathrm{y} = 21.52 \mathrm{g} \\ \mathrm{mass} \mathrm{of} \mathrm{Neon} = \frac{\mathrm{Massof} \mathrm{neon}}{\mathrm{Total} \mathrm{mass}} \times 100 \\ = \frac{8.48}{30} \times 100 = 28.3\% \end{gathered}$$

$$\begin{gathered} \mathrm{The} \mathrm{van} \mathrm{der} \mathrm{Waal}\text{'}\mathrm{s} \mathrm{equation} \mathrm{for} 1 \mathrm{mole} \mathrm{of} \mathrm{gas} \mathrm{is} \\ \left(\mathrm{P}+\frac{\mathrm{a}}{{\mathrm{V}}^2}\right) \left(\mathrm{V}-\mathrm{b}\right)=\mathrm{RT} \\ \mathrm{if} \mathrm{we} \mathrm{put}, {\mathrm{P}}_{\mathrm{r}}=\frac{\mathrm{P}}{{\mathrm{P}}_{\mathrm{C}}}, {\mathrm{V}}_{\mathrm{r}}=\frac{{\mathrm{V}}_{\mathrm{m}}}{{\mathrm{V}}_{\mathrm{c}}} \mathrm{and} {\mathrm{T}}_{\mathrm{r}}=\frac{\mathrm{T}}{{\mathrm{T}}_{\mathrm{C}}}; \\ \left(\because {\mathrm{P}}_{\mathrm{C}}=\frac{\mathrm{a}}{27 {\mathrm{b}}^2}, {\mathrm{V}}_{\mathrm{C}}=3\mathrm{b} \mathrm{and} {\mathrm{T}}_{\mathrm{C}}=\frac{8\mathrm{a}}{27 \mathrm{Rb}}\right) \\ \left({\mathrm{P}}_{\mathrm{r}}\left(\frac{{\mathrm{a}}^2}{27 {\mathrm{b}}^2}\right)+\frac{\mathrm{a}}{{\mathrm{V}}_{\mathrm{r}}^2{\left(3\mathrm{b}\right)}^2}\right) \left({\mathrm{V}}_{\mathrm{r}}\left(3\mathrm{b}\right)-\mathrm{b}\right)={\mathrm{RT}}_{\mathrm{r}} \left(\frac{8\mathrm{a}}{27\mathrm{Rb}}\right) \\ \mathrm{This} \mathrm{equation} \mathrm{is} \mathrm{called} \mathrm{van} \mathrm{der} \mathrm{Waal}\text{'}\mathrm{s} \mathrm{equation} \mathrm{of} \mathrm{law} \mathrm{of} \mathrm{corresponding} \mathrm{states}. \end{gathered}$$

(C)  $\mathrm{V} \mathrm{\alpha } \mathrm{n}$ समान ताप तथा दाब पर।