What is the root-mean-square speed of chlorine gas molecules at a temperature of 320 K? (R = 8.31 J/mol*K,N_A = 6.02 x 10²³,and the molecular mass of Cl₂ = 71) A)1.7 x 10² m/s B)3.4 x 10² m/s C)0.8 x 10⁴ m/s D)1.1 x 10⁵ m/s

Question

Quizplus · Accepted Answer

The root-mean-square speed (urms) of a gas molecule can be calculated using the formula:

urms = √(3RT/M)

where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.

Plugging in the values given:

R = 8.31 J/mol•K
T = 320 K
M = 71 g/mol = 0.071 kg/mol

urms = √(3(8.31 J/mol•K)(320 K)/(0.071 kg/mol))
urms = 339.83 m/s

Rounding to two significant figures, the answer is approximately 3.4 x 10^2 m/s, which is choice B.

What Is the Root-Mean-Square Speed of Chlorine Gas Molecules at a Temperature