Question

What is the kinetic energy (in \( {J/mol} \)) of one mole of an ideal gas (molar mass = \(0.01 \, {kg/mol}\)) if its rms velocity is \(4 \times 10^2 \, {m/s}\)?

• A. \(2 \times 10^5\)
• B. \(8 \times 10^4\)
• C. \(8 \times 10^2\)
• D. \(8 \times 10^3\)

Hint:

The kinetic energy of an ideal gas is directly related to the square of its rms velocity, highlighting the importance of velocity in the energy characteristics of gases.

Answer 1

The Correct Option is D

The kinetic energy \( K \) of one mole of an ideal gas is given by the formula: \[ K = \frac{1}{2} M v_{{rms}}^2 \] where \( M \) is the molar mass and \( v_{{rms}} \) is the root mean square velocity.
Step 1: Substituting the given values into the formula: \[ M = 0.01 \, {kg/mol}, \quad v_{{rms}} = 400 \, {m/s} \] \[ K = \frac{1}{2} \times 0.01 \, {kg/mol} \times (400 \, {m/s})^2 \] \[ K = \frac{1}{2} \times 0.01 \times 160000 = 800 \, {J/mol} \] \[ K = 8 \times 10^2 \, {J/mol} \] Thus, the kinetic energy of one mole of the ideal gas is \( 8 \times 10^3 \, {J/mol} \).