Question

If \(p\), \(T\), \(\rho\) and \(R\) represents pressure, temperature, density and universal gas constant respectively, then the molar mass of the ideal gas is given by

• A. \(\frac{\rho RT}{p}\)
• B. \(\frac{\rho T}{pR}\)
• C. \(\frac{p}{RT\rho}\)
• D. \(\frac{RT}{p\rho}\)

Hint:

Density \(\rho = pM/RT\), so \(M = \rho RT/p\).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Ideal gas equation: \(pV = nRT\), and \(n = m/M\).
Step 2: Detailed Explanation:
\(pV = (m/M)RT \rightarrow M = (mRT)/(pV) = \rho RT/p\)
Step 3: Final Answer:
\(M = \rho RT/p\).