The ratio of root mean square velocity of hydrogen at 50 ~K to that of nitrogen at 500 ~K is closest to

Correct answer: (A) 1.18. V_rms=√((3 RT)/M) frac (V_rms )_H_2 (~V_rms )_O_2=(√((3 × R × 50)/2))/(√((3 × R × 500)/28))=1.18

Q27 / 90 · KVPY 2016 (SB/SX) · Chemistry

The ratio of root mean square velocity of hydrogen at $50 \mathrm{~K}$ to that of nitrogen at $500 \mathrm{~K}$ is closest to

Correct answer
A
$1.18$
B
$0.85$
C
$0.59$
D
$1.40$

Solution

$\mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}$ $\frac{\left(\mathrm{V}_{\mathrm{rms}}\right)_{\mathrm{H}_{2}}}{\left(\mathrm{~V}_{\mathrm{rms}}\right)_{\mathrm{O}_{2}}}=\frac{\sqrt{\frac{3 \times \mathrm{R} \times 50}{2}}}{\sqrt{\frac{3 \times \mathrm{R} \times 500}{28}}}=1.18$

Hence, the correct answer is option: 'A'.

More States of Matter Questions

Among the following, the plot that shows the correct marking of most probable velocity V MP , average velocity V , and root mean square velo2020 (SA)
The isotherms of a gas are shown below : Among the following, (i) At T 1 , the gas cannot be liquefied (ii) At point B , liquid starts to ap2020 (SA)
For one mole of a van der Waals gas, the compressibility factor Z = p V R T at a fixed volume will certainly decrease, if [Given : a and b a2019 (SA)
A container of volume 2 . 24 L can with stand a maximum pressure of 2 atm at 298 K before exploding. The maximum amount of nitrogen (in g ) 2018 (SA)
The pressure p and volume V isotherm of a van der Waals gas, at the temperature at which it undergoes gas to liquid transition, is correctly2018 (SB/SX)
At a constant pressure , the plot of volume as a function of temperature for 2 moles of an ideal gas gives a straight line with a slope . Th19 Nov, 2017 (SA)