The pressure of sulfur dioxide (SO2) is 2.27 x 104 Pa. There are 418 moles of this gas in a volume of 57.9 m3. Find the translational rms speed of the sulfur dioxide molecules.

The translational rms speed of the sulfur dioxide molecules. vrms = 52.8 m/s

Explanation:

The root-mean-square speed is the measure of the speed of particles in a gas. It is given by the formula below;

vrms=√3RT/M

where vrms is the root-mean-square of the velocity, M is the molar mass of the gas in kilograms per mole, R is the molar gas constant, and T is the temperature in Kelvin.

Molar mass of SO₂ in Kg / mole = (64/1000) Kg/mol = 0.064 kg/mol

R = 8.314 m³. Pa/K*mol

T = ?

Using PV = nRT to find T

T = PV/nR

Substituting for T in the rms formula

vrms = √ (3R*PV/nR) / M

vrms = √3PV/nM

vrms = √3 * 2.27 * 10⁴ * 57.9) / 418 * 0.064

vrms = 52.8 m/s