Question

a sample of an idea gas has a volume of 3.65 L at 11.20 C and 1.70 atm. What is the volume of the gas at 18.40 C at 0.998 atm

Answer 1

Given Data:

For first condition: V₁ = 3.65 L, T₁ = 11.20 ^oC = 284.35 K, P₁ = 1.70 atm

For second condition: T₂ = 18.40 ^oC = 291.55 K, P₂ = 0.998 atm, V₂= ?

Solution:

Ideal gas law: PV = nRT

For first condition: P₁V₁ = nRT₁ ................. (i)

For second Condition P₂V₂ = nRT₂ ............(ii)

Note that, n, R are constant for both conditions

Now divide equation (ii) by (i)

(P₂V₂) / (P₁V₁) = (nRT₂) / (nRT₁)

solving for V₂ gives

V₂ = (T₂/T₁) . (P₁/P₂). V₁

= (291.55/284.35) . (1.70/0.998) . (3.65)

V₂ = 6.375 L

Volume of gas at 18.40 ^oC & 0.998 atm is 6.375 L