How to Calculate Volume of Gas Using Combined Gas Law

What is the volume of a sample of gas at different pressure and temperature?

A sample of n2 gas has a volume of 27.0 L at a pressure of 1.50 atm and a temperature of 23°C. What volume in liters will the gas occupy at 3.50 atm and 266°C? Assume ideal behavior.

Answer:

The volume the gas will occupy at 3.50 atm and 266°C is approximately 21.07 liters.

To calculate the volume of a gas sample at different pressure and temperature, we can use the combined gas law formula: (P₁V₁)/T₁ = (P₂V₂)/T₂, where P represents pressure, V represents volume, and T represents temperature in Kelvin.

First, we need to convert the given temperatures to Kelvin:

T₁ = 23°C + 273.15 = 296.15 K

T₂ = 266°C + 273.15 = 539.15 K

Next, we can plug the given values into the formula: (1.50 atm * 27.0 L) / 296.15 K = (3.50 atm * V₂) / 539.15 K

Solving for V₂:

V₂ = (1.50 atm * 27.0 L) * 539.15 K / (296.15 K * 3.50 atm)

V₂ ≈ 21.07 L

Therefore, the gas will occupy a volume of approximately 21.07 liters at 3.50 atm and 266°C, assuming ideal behavior.