Answer:
3.39
Explanation:
Given that
Volume, v = 3.92*10^3 cm³ we convert the volume from cm³ to m³ and we have 0.00392
Pressure, P = 1.25*10^5 Pa
Average Kinetic Energy, K.E = 3.6*10^-22 J
We use the gas law formula,
PV = nRT
Making n subject of the formula, we have
n = PV/RT
Solving for n, we have
n = (1.25*10^5 Pa * 0.00392 m³) / 8.314 * T
n = 4.9*10^8 / 8.314 * T
n = 490 / 8.314T
n = 58.94/T
Note that average kinetic energy is given as
K.E(avg) = 3/2K.T,
3/2 K.T = 3.6*10^-22 J
where K = 1.38*10^-23
T = (3.6*10^-22 J * 2) / (3 * 1.38*10^-23)
T = 17.39
Substitute for T, we have
n = 58.94 / 17.39
n = 3.39