What pressure does gas exert at a temperature of 17`C in a container with a capacity of 2 liters

What pressure does gas exert at a temperature of 17`C in a container with a capacity of 2 liters, if it consists of 2 * 10 ^ 22 molecules?

To determine what pressure p the gas exerts at a temperature of T = 17 ° C = (273 + 17) K = 290 K in a vessel with a capacity of V = 2 L = 0.002 m ^ 3, if it consists of N = 2 ∙ 10 ^ 22 molecules , we use the Mendeleev-Clapeyron equation: р ∙ V = R ∙ T ∙ N / Na, where the universal gas constant R = 8.3 J / (mol ∙ K), and Avogadro’s number Na = 6.02 ∙ 10 ^ 23 mol ^ (- one). Means:

p = R ∙ T ∙ N / (Na ∙ V).

Substitute the values of the quantities into the calculation formula:

p = 8.3 J / (mol ∙ K) ∙ 290 K ∙ 2 ∙ 10 ^ 22 / (6.02 ∙ 10 ^ 23 mol ^ (- 1) ∙ 0.002 m ^ 3);

p ≈ 40,000 Pa = 40 kPa.

Answer: the gas exerts a pressure equal to 40 kPa.