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

| February 3, 2021 | education

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.

V = 10 l = 10 * 10 ^ -3 m3.

T = 300 ° C.

ΔР = 4.2 kPa = 4200 Pa.

NA = 6 * 10 ^ 23 mol − 1.

R = 8.31 m2 * kg / s2 * ° K * mol.

ΔN -?

With a gas leak, the volume of gas in the cylinder V and its temperature T remains unchanged, therefore the Mendeleev-Cliperon equation before and after the leak will look like: P1 * V = v1 * R * T, P2 * V = v2 * R * T.

ΔР = Р1 – Р2 = v1 * R * T / V – v2 * R * T / V = ​​(v1 – v2) * R * T / V.

Let us express the change in the amount of substance: Δv = (v1 – v2) = ΔР * V / R * T.

By definition, the amount of substance is expressed by the formula: v1 = N1 / Na, v2 = N2 / Na.

(v1 – v2) = ΔP * V / R * T.

N1 / Nа – N2 / Nа = ΔР * V / R * T.

(N1 – N2) / Na = ΔР * V / R * T.

ΔN = (N1 – N2) = ΔР * V * Na / R * T.

ΔN = 4200 Pa * 10 * 10 ^ -3 m3 * 6 * 10 ^ 23 mol − 1 / 8.31 m2 * kg / s2 * ° K * mol * 300 ° K = 101.08 * 1020.

Answer: when gas leaks from the cylinder, ΔN = 101.08 * 1020 came out of it.



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