The rms speed of Molecules in a gas sample can be changed by — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

I need to see the answer options to explain why C is correct. Since they're not provided in your question, let me work through the physics of rms speed and identify what typically changes it. **RMS Speed Formula:** $$v_{rms} = \sqrt{\frac{3kT}{m}} = \sqrt{\frac{3RT}{M}}$$ where $T$ is temperature, $M$ is molar mass, $R$ is the gas constant, and $k$ is Boltzmann's constant. **What CHANGES rms speed:** - **Temperature (T):** $v_{rms} \propto \sqrt{T}$ — Increasing temperature increases rms speed ✓ - **Molar mass (M):** $v_{rms} \propto \frac{1}{\sqrt{M}}$ — For a fixed gas ($N_2$), this is constant ✗ - **Pressure/Volume:** These don't directly affect rms speed (only indirectly through temperature via ideal gas law) ✗ **Most likely answer C is:** ***Changing the temperature*** of the gas sample. This is the only intensive variable that directly affects rms speed. Pressure, volume, or number of molecules don't change $v_{rms}$ for the same gas at the same temperature. --- *If you can provide the actual options (A, B, C, D), I can give a more precise explanation of why C is correct and why others fail.*