Question

What is the root-mean-square speed of chlorine gas molecules at a temperature of 320 K? (R = 8.31 J/mol⋅K, NA = 6.02 × 10^23, and the molecular mass of Cl2 = 71) a. 1.7 × 102 m/sb. 3.4 × 102 m/sc. 0.8 × 104 m/sd. 1.1 × 105 m/s

Answer 1

b. 3.4 × 10^2 m/s

Step-by-step explanation:

The rms speed of a gas is given by

`v_{\text{rms}}=\sqrt[]{(3RT)/(M_m)}`

where R = gas constant = 8.31 J/mol⋅K, T = temperature, and Mm = molar mass in kg/mol

Now in our case, we have

T = 320 K and Mm = 71g/mol = 0.071 kg / mol; therefore, the above equation gives

`v_{\text{rms}}=\sqrt[]{(3(8.31)(320))/(0.071)}`
`\boxed{v_{\text{rms}}=3.4\cdot10^4m/s}`

which is our answer!

Hence, choice B is the correct answer.