In a cylinder with a capacity of 10 liters, there is gas at a temperature of 27 degrees due to a gas leak

In a cylinder with a capacity of 10 liters, there is gas at a temperature of 27 degrees due to a gas leak, the pressure in the cylinder has dropped to 4.2 kPa How many molecules have left the cylinder? Consider the temperature unchanged.

The state of the gas is described by the Mendeleev – Clapeyron equation, p * v = η * R * T p – pressure, v – volume, η – number of moles, R – universal gas constant, T – temperature.

Since the temperature and volume have not changed, the equality is true:

Δp * v = Δη * R * T – Δp is the change in pressure, Δη is the number of moles of the escaped gas.

Δη = Δp * v / R * T = (p1 – p2) * v / R * T, p1 – initial pressure (not specified in the problem).

We find the number of molecules by the formula:

N = Na * η, where Na is Avogadro’s number.