Step 1: Recall the kinetic theory expression for kinetic energy of an ideal gas.
For one mole of an ideal gas, the average kinetic energy is: \[ KE = \frac{3}{2}RT \] where $R$ is the universal gas constant and $T$ is the absolute temperature.
Step 2: Identify what KE depends on.
From the formula $KE = \frac{3}{2}RT$, the kinetic energy of 1 mole of an ideal gas depends ONLY on the temperature $T$, not on the molar mass or the nature of the gas.
Step 3: Evaluate the false statement about ideal gases.
A statement claiming that the kinetic energy of 1 mol of an ideal gas depends on the molar mass (or molecular mass) of the gas would be FALSE. All ideal gases at the same temperature have the same molar kinetic energy.
Step 4: Explain why mass does not matter.
In kinetic theory, higher molar mass gases have lower average speeds, but the kinetic energy ($\frac{1}{2}mv^2$ per molecule) averages out to the same value $\frac{3}{2}k_BT$ per molecule regardless of $m$, because $v^2$ adjusts inversely with $m$.
Step 5: Contrast with real gas behavior.
For real gases, intermolecular attractions affect total energy, but for ideal gases, no intermolecular forces exist, so KE alone represents internal energy, and it depends only on $T$.
Step 6: Conclude which option is false.
The statement that the KE of 1 mol of ideal gas depends on the mass of the molecule is the FALSE statement.
\[ \boxed{\text{Option 1 is false: KE of ideal gas depends only on } T, \text{ not mass}} \]