# A vessel with a volume of V = 30 l contains ideal gas at a temperature of 0 ° C. After part of the gas was released

A vessel with a volume of V = 30 l contains ideal gas at a temperature of 0 ° C. After part of the gas was released outside, the pressure in the vessel dropped by DP = 0.78 atm without changing the temperature. Find the mass of the released gas. The density of this gas under normal conditions is considered equal to 1.3 · 10-3 kg / l.

Let m1 and m2 be the gas masses in the vessel before and after gas release. Thus, the mass of the gas emitted can be found using the following formula:
Δm = m1 – m2;
Now from the ideal gas equation, we can derive the following formula:
p * V = m1 * (R / M) * T.
since V and T are the same before and after gas release.
1. (p1 – p2) * V = (m1 – m2) * RMT = Δm * RMT * (p1 – p2) * V = (m1 – m2) * RMT = Δm * RMT;
2. Δm = (p1 – p2) * V * MRT = Δp * VMR * T * Δm = (p1 – p2) * V * MRT = Δp * V * MRT;
From equations (1) and (2) we obtain the following:
Δm = ρV * Δp * p0 = 1.3 ⋅ 30 ⋅ 0.781 = 30 g.