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 Calculation **Key Principle:** Molar kinetic energy depends only on temperature, not on the amount or type of gas. The average molar kinetic energy is: $$KE_{molar} = \frac{3}{2}RT$$ where $R$ is the gas constant and $T$ is absolute temperature. **Setting up the equation:** For He at temperature $T_{He}$: $$KE_{He} = \frac{3}{2}RT_{He}$$ For Ar at 400 K: $$KE_{Ar} = \frac{3}{2}R(400)$$ **Since molar KE must be equal:** $$\frac{3}{2}RT_{He} = \frac{3}{2}R(400)$$ $$T_{He} = 400 \text{ K}$$ **Explanation:** The molar kinetic energy is **independent of the number of moles and the identity of the gas**—it depends only on temperature. Since we want equal molar kinetic energies, both gases must be at the **same temperature**. Therefore, He must also be at **400 K**. *(Note: The given information about 0.3 mol and 0.4 mol is a distractor—these amounts do not affect molar kinetic energy.)* **Answer: D (400 K)**