Question

At \(T\)(K), the pressure of two ideal gases \(A\) and \(B\) is in the ratio \[ P_A:P_B=2:5. \] At this temperature, their densities are the same. The molar mass ratio \[ (M_A:M_B) \] is

• A. \(5:2\)
• B. \(1:2\)
• C. \(5:1\)
• D. \(25:4\)

Hint:

For an ideal gas, \[ \boxed{ \rho=\frac{PM}{RT}. } \] At the same temperature, if two gases have equal densities, \[ \boxed{ P_1M_1=P_2M_2. } \]

Answer 1

The Correct Option is A

Step 1: Use the ideal gas density relation. For an ideal gas, \[ \rho=\frac{PM}{RT}. \] Since both gases have the same density and temperature, \[ \frac{P_AM_A}{RT} = \frac{P_BM_B}{RT}. \] Therefore, \[ P_AM_A=P_BM_B. \]

Step 2: Substitute the pressure ratio. Given, \[ P_A:P_B=2:5. \] Hence, \[ 2M_A=5M_B. \] Therefore, \[ M_A:M_B = 5:2. \]

Step 3: Write the answer. Hence, \[ \boxed{5:2}. \] Thus, \[ \boxed{(A)} \] is the correct answer.