Question

A sample of 4 mol of diatomic gas is measured to have a temperature of 290 K. If the mass of the gas is 0.064 kg, what is the approximate average speed of the molecules in the gas? (Recall that the equation for kinetic energy due to translation in a gas is KEtranslational - 1 3 nRT, and R = 8.31 J/(mol. 2 2. K).) mv2A. 599 m/sB. 672 m/sC. 643 m/sD. 699 m/s

Answer 1

Given

Number of moles, n=4 mol

The temperature is T=290K

Mass of the gas, m=0.064 kg

Universal gas constant, R=8.31 J/mol.K

To find

The average speed of the molecule

Explanation

The average speed is given by

$\begin{gathered} v=\sqrt{\frac{3nRT}{m}} \\ \Rightarrow v=\sqrt{\frac{3\times4\times8.31\times290}{0.064}} \\ \Rightarrow v=672.19\text{ m/s} \end{gathered}$

Conclusion

The average speed is B. 672 m/s