A container having a volume of 1 m3
holds
90 mol of helium gas at 176
◦
C.
Boltzmann’s constant is 1.38 × 10
−23
J/K.
Assuming the helium behaves like an ideal
gas, what is the average kinetic energy per
molecule?
Answer in units of J
32
To find the average kinetic energy per molecule of helium gas, we can use the equation:
Average kinetic energy per molecule = (3/2) * k * T
where:
- k is Boltzmann's constant (1.38 × 10^-23 J/K)
- T is the temperature in Kelvin
First, we need to convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 176 °C + 273.15
T(K) = 449.15 K
Now that we have the temperature in Kelvin, we can substitute the values into the equation:
Average kinetic energy per molecule = (3/2) * (1.38 × 10^-23 J/K) * 449.15 K
Calculating the expression:
Average kinetic energy per molecule = (3/2) * (1.38 × 10^-23 J/K) * 449.15 K
Average kinetic energy per molecule ≈ 9.19 × 10^-21 J
Therefore, the average kinetic energy per molecule of helium gas is approximately 9.19 × 10^-21 J.