Question

The density of a gas \(X\) is twice that of another gas \(Y\). If the molecular weight of gas \(Y\) is \(M\), then the molecular weight of the gas \(X\) will be

• A. \(2M\)
• B. \(\frac{M}{2}\)
• C. \(M\)
• D. \(\frac{M}{4}\)

Hint:

At same temperature and pressure, gas density is proportional to molecular weight: \(\rho\propto M\).

Answer 1

The Correct Option is A

For gases at the same temperature and pressure, density is directly proportional to molecular weight. That is: \[ \rho \propto M. \] Given that density of gas \(X\) is twice that of gas \(Y\): \[ \rho_X=2\rho_Y. \] Therefore, molecular weight of gas \(X\) will also be twice that of gas \(Y\): \[ M_X=2M_Y. \] Given: \[ M_Y=M. \] So: \[ M_X=2M. \] Therefore, the molecular weight of gas \(X\) is: \[ 2M. \]