Question

Identify the correct relationship between pressure (P), density (d), molar mass (M) and Temperature (T) for an ideal gas from the following.

• A. \(P = \frac{d\times M\times R}{T}\)
• B. \(P = \frac{d\times R\times T}{M}\)
• C. \(P = \frac{M\times R\times T}{d}\)
• D. \(P = \frac{d\times M\times T}{R}\)

Hint:

Start from PV = nRT and replace n by mass over molar mass.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
The ideal gas equation is \( PV = nRT \) with \( n = \frac{m}{M} \).

Step 2: Derivation
\( PV = \frac{m}{M}RT \Rightarrow P = \frac{m}{V}\cdot\frac{RT}{M} \).
Since density \( d = \frac{m}{V} \), we get \( P = \frac{dRT}{M} \).

Step 3: Compare the options
This matches option (B).

Final Answer:
The correct relation is P = dRT/M. \[ \boxed{\text{(B) }P = \dfrac{d\times R\times T}{M}} \]