A sample of neon gas has a root mean square (rms) speed of 500.0 m/s. What is the temperature (in kelvin) of the sample? (Molar mass of neon = 20.18 g/mol)

• A. 126 K
• B. 100 K
• C. 252 K
• D. 504 K

Answer: (C)

Verified step by step guidance

1. Recall the formula for the root mean square (rms) speed of a gas: \(v_{rms} = \sqrt{\frac{3RT}{M}}\), where \(v_{rms}\) is the rms speed, \(R\) is the ideal gas constant, \(T\) is the temperature in kelvin, and \(M\) is the molar mass in kilograms per mole.
2. Convert the molar mass of neon from grams per mole to kilograms per mole by dividing by 1000: \(M = \frac{20.18}{1000} \text{ kg/mol}\).
3. Rearrange the rms speed formula to solve for temperature \(T\): \(T = \frac{M v_{rms}^2}{3R}\).
4. Substitute the known values into the equation: use \(v_{rms} = 500.0 \text{ m/s}\), \(M\) in kg/mol, and \(R = 8.314 \text{ J/(mol\cdot K)}\).
5. Calculate the temperature \(T\) using the substituted values to find the temperature of the neon gas sample in kelvin.