Question

A cylinder of an ideal gas contains 1.2 moles of gas and occupies a volume of 5.0L. If 0.5 moles of a second gas are added to the cylinder, and the cylinder is allowed to expand until it reaches the same temperature and pressure as before, what is the final volume of gas, in liters, that occupies the cylinder?

Answer 1

7.08 L

Step-by-step explanation:

From the question given above, the following data were obtained:

Initial mole (n₁) = 1.2 moles

Initial volume (V₁) = 5 L

Final mole (n₂) = 1.2 + 0.5 = 1.7 moles

Final volume (V₂) =?

From ideal gas equation,

PV = nRT

Divide both by n

PV / n = RT

Divide both side by P

V / n = RT/P

RT/P => constant

Therefore,

V₁ / n₁ = V₂ / n₂

With the above formula i.e

V₁/n₁ = V₂/n₂

We can obtain the final volume of the gas as follow:

Initial mole (n₁) = 1.2 moles

Initial volume (V₁) = 5 L

Final mole (n₂) = 1.7 moles

Final volume (V₂) =?

V₁/n₁ = V₂/n₂

5 / 1.2 = V₂ / 1.7

Cross multiply

5 × 1.7 = 1.2 × V₂

8.5 = 1.2 × V₂

Divide both side by 1.2

V₂ = 8.5 / 1.2

V₂ = 7.08 L

Therefore, the final volume of the gas is 7.08 L