Question

Which of the following do you think is a correct relationship between the molar mass of gas temperature and its pressure?

(a) M = dRT/P

(b) M = dRT/V

(c) PV = nRT

(d) M = VRT/P

The question was posed to me by my college director while I was bunking the class.

This question is from States of Matter in portion States of Matter of Chemistry – Class 11

Answer 1

The correct relationship between the molar mass ($M$) of a gas, its density ($d$), temperature ($T$), and pressure ($P$) is given by:

(a) M=dRTPM = \frac{dRT}{P}M=PdRT​

Explanation:

This equation is derived from the ideal gas law:

$$PV=nRT$$

Where:

• $P$ = pressure,
• $V$ = volume,
• $n$ = number of moles,
• $R$ = universal gas constant,
• $T$ = temperature.

Using the definition of molar mass $M$ and density $d$:

1. Number of moles, n=massMn = \frac{\text{mass}}{M}n=Mmass​,
2. Density, d=massVd = \frac{\text{mass}}{V}d=Vmass​.

Substitute n=dVMn = \frac{dV}{M}n=MdV​ into the ideal gas law:

P⋅V=d⋅VM⋅R⋅TP \cdot V = \frac{d \cdot V}{M} \cdot R \cdot TP⋅V=Md⋅V​⋅R⋅T

Cancel $V$ from both sides:

P=dRTMP = \frac{dRT}{M}P=MdRT​

Rearranging for $M$:

M=dRTPM = \frac{dRT}{P}M=PdRT​

Thus, the correct answer is (a).

Would you like additional clarification on how this equation applies to real-world scenarios?