Question

The average molecular speed is greatest in which of the following gas samples ?

• A. 1.0 mole $N_2$ at 560 K
• B. 0.50 mole of Neat 500 K
• C. 0.20 mole $CO_2$ at 440 K
• D. 2.0 mole of He at 140 K

Answer 1

Answer: (D)

2.0 mole of He at 140 K

Answer 2

$\bar{\upsilon} (Ne) = \left( \frac{8R \times 560}{\pi \times 28} \right) ^{\frac{1}{2}}$ (A) $\bar{\upsilon} (N_2) = \left( \frac{8R \times 560}{\pi \times 28} \right) ^{\frac{1}{2}} = \left( \frac{160 \, R}{\pi}\right)^{\frac{1}{2}}$ (B) $\bar{\upsilon} (Ne) = \left( \frac{8R \times 500}{\pi \times 20} \right) ^{\frac{1}{2}} = \left( \frac{200 \, R}{\pi}\right)^{\frac{1}{2}}$ (C) $\bar{\upsilon} (CO_2) = \left( \frac{8R \times 440}{\pi \times 44} \right) ^{\frac{1}{2}} = \left( \frac{80 \, R}{\pi}\right)^{\frac{1}{2}}$ (D) $\bar{\upsilon} (He) = \left( \frac{8R \times 140}{\pi \times 4} \right) ^{\frac{1}{2}} = \left( \frac{280 \, R}{\pi}\right)^{\frac{1}{2}}$ Thus, $\upsilon(He)$ is maximum .