Question

What is the temperature of CO2 gas if the average speed (actually the root-mean-square speed) of the molecules is 750 m/s?

Answer 1

Answer:

992.302 K

Explanation:

V(rms) = 750 m/s

V(rms) = √(3RT / M)

V = velocity of the gas

R = ideal gas constant = 8.314 J/mol.K

T = temperature of the gas

M = molar mass of the gas

Molar mass of CO₂ = [12 + (16*2)] = 12+32 = 44g/mol

Molar mass = 0.044kg/mol

From

½ M*V² = 3 / 2 RT

MV² = 3RT

K = constant

V² = 3RT / M

V = √(3RT / M)

So, from V = √(3RT / M)

V² = 3RT / M

V² * M = 3RT

T = (V² * M) / 3R

T = (750² * 0.044) / 3 * 8.314

T = 24750000 / 24.942

T = 992.302K

The temperature of the gas is 992.302K

Note : molar mass of the gas was converted from g/mol to kg/mol so the value can change depending on whichever one you use.