Question

The diagram shows the Maxwell’s speed distribution curves for a certain ideal gas at two different temperature $T_1$ and $T_2$. Pick the correct options:
Take $R=\frac{1}{12}\text{L atm/molK}$

• A. At 400 K, most probable speed is 800 m/s
• B. At 400 K, rms speed is 1000 m/s
• C. $T_2=600K$
• D. $M=5g/mol$

Answer 1

Answer: (B), (C)

$T_2=600K$

$c_{mp}=\sqrt{\frac{2RT}{M}}{c}_{rms}=\sqrt{\frac{3RT}{M}}$
At $150K,c_{mp}=500m{s}^{-1}\Rightarrow 500=\sqrt{\frac{2RT}{M}}=\sqrt{\frac{2\times 25/3\times 150}{M}}\Rightarrow M=10\times {10}^{-3}kg=10g/mol$
At $T_2,c_{mp}=1000m{s}^{-1}\Rightarrow 1000=\sqrt{\frac{2\times 25/3T_2}{10\times 10-3}}\Rightarrow T_2=600K$
At $400K,c_{rms}=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3\times 25/3\times 400}{10\times {10}^{-3}}}=1000m{s}^{-1}$

$c_{mp}=\sqrt{\frac{2RT}{M}}=\sqrt{\frac{2\times 25/3\times 400}{10\times {10}^{-3}}}\approx 800m{s}^{-1}$