# How many molecules are in a vessel with a capacity of 450 cm ^ 3 at a temperature of 20 C and a pressure of 25 kPa?

V = 450 cm ^ 3 = 45 * 10 ^ 5 m ^ 3.

T = 293 ° C.

P = 25 kPa = 25 * 10 ^ 3 Pa.

Na = 6 * 10 ^ 23 mol ^ -1.

R = 8.31 m ^ 2 * kg / s ^ 2 * K * mol.

N -?

Let us write the Mendeleev-Cliperon law: P * V = m * R * T / M, where P is the pressure of the substance, V is the volume, m is the mass of the substance, R is the universal gas constant, T is the absolute temperature, M is the molar mass of the substance.

The amount of substance v is called the ratio: v = m / M.

P * V = v * R * T.

v = P * V / R * T.

The amount of substance v can be expressed by another formula: v = N / Na, where N is the number of molecules, Na is Avogadro’s number.

N / Na = P * V / R * T.

N = P * V * Na / R * T.

N = 25 * 10 ^ 3 Pa * 45 * 10 ^ 5 m ^ 3 * 6 * 10 ^ 23 mol ^ -1 / 8.31 m ^ 2 * kg / s ^ 2 * K * mol * 293 ° K = 2 , 77 * 10 ^ 31.

Answer: the vessel contains N = 2.77 * 10 ^ 31 molecules.