Calculate the root mean square speed of gaseous krypton atoms at 27 °C. Given that the molar mass of krypton is 83.8 g/mol, which of the following is the correct root mean square speed?

• A. 400 m/s
• B. 300 m/s
• C. 200 m/s
• D. 500 m/s

Answer: (D)

Verified step by step guidance

1. Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature in Celsius: \( T = 27 + 273.15 \).
2. Use the formula for root mean square speed \( v_{rms} = \sqrt{\frac{3RT}{M}} \), where \( R \) is the ideal gas constant \( 8.314 \text{ J/mol·K} \), \( T \) is the temperature in Kelvin, and \( M \) is the molar mass in kg/mol.
3. Convert the molar mass of krypton from grams per mole to kilograms per mole by dividing by 1000: \( M = \frac{83.8}{1000} \text{ kg/mol} \).
4. Substitute the values into the root mean square speed formula: \( v_{rms} = \sqrt{\frac{3 \times 8.314 \times T}{M}} \).
5. Calculate the expression inside the square root and then take the square root to find the root mean square speed.