A gas sample containing 1.45 mol at 25°C exerts a pressure of 408 torr. Some gas is added to the same container, and the temperature is increased to 50.°C. If the pressure increases to 800. torr, how many moles of gas were added to the container? Assume a constant-volume container.

It were added 1.17 moles of gas

Explanation:

We use the Ideal Gases Law to propose both situations:

P. V = n. R. T

For initial situation → P₁. V₁ = n₁. R. T₁

For the second situation → P₂. V₂ = n₂. R. T₂

R is a constant and V remains constant, so we cancel from the equations.

(n₁. T₁) / P₁ = (n₂. T₂) / P₂

Notice that n₂ = n₁ + x where n₁ = 1.45 moles.

Let's make the conversions for the units

25°C + 273 = 298 K (T₁) and 50°C + 273 = 323K (T₂)

408 Torr. 1 atm / 760 Torr = 0.537 atm (P₁)

800 Torr. 1 atm / 760 Torr = 1.05 atm (P₂)

Let's replace and find the x

(1.45 mol. 298K) / 0.537 atm = ((x + 1.45mol). 323K) / 1.05 atm

(1.45 mol. 298K) / 0.537 atm. 1.05 atm = (x + 1.45mol). 323K

845 mol. K = 323 x K + 468.35 mol. K

845 mol. K - 468.35 mol. K = 323 x K

376.65 mol. K / 323 K = x

1.17 mol = x