Question

Boltzmann’s constant is 1.38066×10−23 J/K, and the universal gas constant is 8.31451 J/K · mol. If 1.9 mol of a gas is confined to a 7.1 L vessel at a pressure of 9 atm, what is the foss (zef86) – Homework 11, Ideal gas, kinetic theory 19-20 – dowd – (PriceEPHY11920 2) 3 average kinetic energy of a gas molecule? Answer in units of J.

Answer 1

Answer:

The average kinetic energy of a gas molecule is 8.49 × 10⁻²¹ J

Explanation:

According to Kinetic Molecular Theory, the average kinetic energy of gas molecules is a function only of temperature and is given by the equation:

$E=\frac{3}{2}kT$

$pV=nRT;\\T=\frac{pV}{nR}$

Substituting the value of T in the kinetic energy equation:

$E=\frac{3kpV}{2nR}$

Where p is the pressure of the gas = 9 atm = 9 × 101325 pa

k is the Boltzmann’s constant  =  1.38066 × 10⁻²³ J/K,

V is the volume of the gas = 7.1 L = 7.1 × 10⁻³ m³

n is the number of moles of the gas = 1.9 mol

R is the universal gas constant = 8.31451 J/K · mol.

E is the average kinetic energy of a gas molecule

Substituting values:

$E=\frac{3kpV}{2nR}=\frac{3*1.38066*10^{-23}*9*101325*7.1*10^{-3}}{2*1.9*8.31451}=8.49*10^{-21}J$

The average kinetic energy of a gas molecule is 8.49 × 10⁻²¹ J