At what temperature will the molar KE of 0.3 mol of He be the same as that of 0.4 mol of argon at 40 — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

# Solution: Molar Kinetic Energy Temperature **Key Concept:** Molar kinetic energy depends only on temperature, not on the amount or type of gas. The molar kinetic energy is given by: $$KE_{molar} = \frac{3}{2}RT$$ where $R$ is the gas constant and $T$ is absolute temperature. **Step 1:** Find molar KE of Ar at 400 K $$KE_{Ar} = \frac{3}{2}R(400)$$ **Step 2:** Set equal to molar KE of He at unknown temperature $T$ $$\frac{3}{2}RT = \frac{3}{2}R(400)$$ **Step 3:** Solve for T $$T = 400 \text{ K}$$ **Explanation:** The molar kinetic energy of any ideal gas depends *only* on temperature through the factor $\frac{3}{2}RT$. It is independent of: - The number of moles (0.3 vs 0.4) - The type of gas (He vs Ar) Therefore, for He and Ar to have the **same molar kinetic energy**, they must be at the **same temperature**. **Answer: D = 400 K**