Find the concentration of the gas in the vessel at a temperature of 100K. if the gas pressure is 1.38MPa.

We translate the values from given to the SI system:
P = 1.38 MPa = 1.38 * 10 ^ 6 Pa.
Let’s use the Mendeleev – Clapeyron equation:
P = n * k * T, where n is the gas concentration, k is the Boltzmann constant k = 1.38 * 10 ^ -23, T is the gas temperature.
Let us express the concentration from this expression:
n = P / (k * T)
Substitute the numerical values and calculate the concentration:
n = P / (k * T) = 1.38 * 10 ^ 6 / (1.38 * 10 ^ -23 * 100) = 1 * 10 ^ 27 1 / m³.
Answer: gas concentration 1 * 10 ^ 27 1 / m³.