Question

55 cubic feet of He at 72ºF and 2000 psig is slowly leaking into a room at 72ºF and 29.85 in Hg atmospheric pressure. What volume will the He occupy?

a) Calculate the volume using the ideal gas law.
b) Determine the volume using Boyle's Law.
c) Find the volume using Charles's Law.
d) Use Gay-Lussac's Law to find the volume.

Answer 1

a) Using the ideal gas law, the volume of He will be 9.1 L. b) Using Boyle's Law, the volume of He will be 145.75 ft³. c) Using Charles's Law, the volume of He will remain at 55 ft³. d) Using Gay-Lussac's Law, the pressure of He will remain at 2.65 atm.

Step-by-step explanation:

a) Using the ideal gas law:

Step 1: Convert the temperature to Kelvin: 72ºF = 22.22ºC = 295.37K

Step 2: Convert the pressure to atm: 2000 psig = 2016.16 mmHg = 2.65 atm

Step 3: Substitute the values into the ideal gas law formula:

V₁ = (n₁RT₁) / P₁

V₁ = (1 mol x 0.0821 L·atm/mol·K x 295.37K) / 2.65 atm = 9.1 L

b) Using Boyle's Law:

Step 1: Convert the pressure to atm: 29.85 in Hg = 1 atm

Step 2: Substitute the values into Boyle's Law formula:

P₁V₁ = P₂V₂

2.65 atm x 55 ft³ = 1 atm x V₂

V₂ = (2.65 x 55) / 1 = 145.75 ft³

c) Using Charles's Law:

Step 1: Convert the temperatures to Kelvin: 72ºF = 295.37K

Step 2: Substitute the values into Charles's Law formula:

V₁ / T₁ = V₂ / T₂

55 ft³ / 295.37K = V₂ / 295.37K

V₂ = 55 ft³

d) Using Gay-Lussac's Law:

Step 1: Convert the temperatures to Kelvin: 72ºF = 295.37K

Step 2: Convert the pressure to atm: 2000 psig = 2.65 atm

Step 3: Substitute the values into Gay-Lussac's Law formula:

P₁ / T₁ = P₂ / T₂

2.65 atm / 295.37K = P₂ / 295.37K

P₂ = 2.65 atm