Determine the number of molecules of an ideal gas, the temperature of which is 290 K

Determine the number of molecules of an ideal gas, the temperature of which is 290 K and the pressure of 4 kPa in the vessel is v = 1.6 liters.

Data: T (ideal gas temperature) = 290 K; P (gas pressure) = 4 kPa (4 * 10 ^ 3 Pa); V (capacity of the vessel in which the gas is located) = 1.6 liters (1.6 * 10 ^ -3 m3).

Reference values: k (Boltzmann’s constant) = 1.38 * 10 ^ -23 J / K.

The number of ideal gas molecules is determined from the formula: P = n * k * T = (N / V) * k * T, whence N = P * V / (k * T).

Let’s calculate: N = 4 * 10 ^ 3 * 1.6 * 10 ^ -3 / (1.38 * 10 ^ -23 * 290) = 16 * 10 ^ 20 molecules.

Answer: The number of ideal gas molecules is 16 * 10 ^ 20.