Question

The atomic mass of a nitrogen atom (N) is 14.0 u, while that of an oxygen atom (O) is 16.0 u. Three diatomic gases have the same temperature: nitrogen (N2), oxygen (O2), and nitric oxide (NO). Rank these gases in ascending order (smallest first), according to the values of their translational rms speeds.
a. N2, O2, NO

b. O2, NO, N2

c. O2, N2, NO

d. NO, N2, O2

Answer 1

Answer:

c.$O_2,NO,N_2$

Explanation:

We are given that

Atomic mass of nitrogen=14 u

Atomic mass of oxygen=16 u

Molar mass of oxygen gas$(O_2)$=$16\times 2=32$u

Molar mass of nitrogen$(N_2)$=$2\times 14=28 u$

Molar mass of nitric oxide(NO)=16+14=30 u

Translational rms speed=$v=\sqrt{\frac{3RT}{M}}$

Where R=Gas constant

M=Molar mass

T=Temperature (in K)

Rms speed is inversely proportional to square root of molar mass

$v_{rms}\propto\frac{1}{\sqrt M}$

If molar mass is high then translational rms speed is less when the molar mass is less then the translational rms speed is high.

Therefore, the translational rms speed of oxygen is large and translationals rms speed of nitrogen gas is small.

$O_2,NO,N_2$

Option c is true