Which equation correctly relates the molar mass (M), density (d), pressure (P), and temperature (T) of an ideal gas using the ideal gas law?

• A. M = dRT / P
• B. M = dP / RT
• C. M = PRT / d
• D. M = dT / PR

Answer: (A)

Verified step by step guidance

1. Recall the ideal gas law equation: \(\displaystyle PV = nRT\), where \(P\) is pressure, \(V\) is volume, \(n\) is number of moles, \(R\) is the gas constant, and \(T\) is temperature.
2. Express the number of moles \(n\) in terms of mass \(m\) and molar mass \(M\): \(\displaystyle n = \frac{m}{M}\).
3. Rewrite the ideal gas law substituting \(n\): \(\displaystyle PV = \frac{m}{M} RT\).
4. Recognize that density \(d\) is mass per volume: \(\displaystyle d = \frac{m}{V}\), so \(m = dV\).
5. Substitute \(m = dV\) into the equation and solve for \(M\): starting from \(PV = \frac{dV}{M} RT\), rearrange to get \(M = \frac{dRT}{P}\).