In a cylinder with a capacity of 40 liters at a temperature of 288 K and a pressure of 4.9 MPa. Find the mass of carbon dioxide CO2.

Given:

V = 40 l = 0.04 m³;

T = 288 K;

p = 4.9 MPa = 4.9 * 10⁹ Pa;

R = 8.1 J / mol * K;

m (CO₂) =?

Decision:

Let’s use the Mendeleev-Clapeyron equation pV = m / M RT.

Let us express the mass m from this formula:

m = pVM / RT.

Let’s find the unknown molar mass M:

М = m₀ (C) + 2m₀ (O) = 12 + 32 = 44 g / mol.

Substitute all available values into the formula for mass m:

m = 4.9 * 10⁹ Pa * 0.04 m³ * 44 g / mol / 8.1 J / mol * K * 288 K ≈ 3.7 * 10⁶ kg.

Answer: ≈ 3.7 * 10⁶ kg.