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