Question

500 cm³ of a gas at S.T.P is filled in a container of volume 1000 cm³ . Keeping the temperature constant, find the required percentage change in pressure.

Answer 1

A 50 % decrease in pressure is required to fill 500 cm³ of a gas at S.T.P in a container of volume 1000 cm³, keeping the temperautre constant.

• Given, 500 cm³ of a gas is at S.T.P.

=> Initial volume of the gas (V₁) = 500 cm³

Or, V₁ = 500 ml   ( 1 cm³ = 1 ml )

Or, V₁ = 0.5 L

• The standard temperautre and pressure conditions are said to be 273 K and 1 atm respectively.

=> Initial temperautre (T₁) = 273 K,

Initial pressure (P₁) = 1 atm

• Final volume of the gas (V₂) = 1000 cm³

Or, V₂ = 1000 ml = 1 L

• The temperature is kept constant. Therefore, by applying Boyle's Law, the final pressure of the gas can be obtained.

P₁V₁  = P₂V₂     (Boyle's Law)

=> 1 atm × 0.5 L = P₂ × 1 L

=> P₂ = (1 atm × 0.5 L) / 1 L

=> P₂ = 0.5 atm

• Percentage change in pressure = (Change in pressure / Original pressure) × 100 %

• Decrease in pressure = P₁ - P₂ = 1 atm - 0.5 atm = 0.5 atm

• Therefore, % change in pressure =

( 0.5 atm / 1 atm ) × 100 %

Or, % change in pressure = 50 %

• The pressure of the gas has to be decreased by 50 %.