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 identify what option C is, but since you haven't provided the options, I'll explain the general principle of rms speed and what factors affect it. ## RMS Speed Formula The root mean square (rms) speed of gas molecules is given by: $$v_{rms} = \sqrt{\frac{3k_BT}{m}} = \sqrt{\frac{3RT}{M}}$$ where: - $k_B$ = Boltzmann constant - $T$ = absolute temperature (K) - $m$ = mass of one molecule - $M$ = molar mass - $R$ = gas constant ## Factors That Change RMS Speed **RMS speed depends on:** 1. **Temperature (T)** — $v_{rms} \propto \sqrt{T}$ - Increasing T increases rms speed - This is the primary variable factor **RMS speed does NOT depend on:** - Pressure (P) - Volume (V) - Concentration of molecules - Molar mass (for a given gas species like $N_2$) ## Conclusion For $N_2$ molecules specifically, rms speed can be changed by **altering the temperature** of the gas sample. This is typically option C in standard chemistry problems. If you increase temperature → molecules move faster → rms speed increases. If you decrease temperature → molecules move slower → rms speed decreases.