Ideal Gas Law and Volume Calculation

What is the volume of the gas at different conditions?

If a sample of an ideal gas has a volume of 3.50 L at 13.80 °C and 1.50 atm, what will be the volume of the gas at 22.00 °C and 0.993 atm?

Volume Calculation of Ideal Gas

In order to calculate the volume of the gas at different conditions, we need to apply the combined gas law equation that relates the initial and final conditions of temperature, pressure, and volume for an ideal gas.

The combined gas law equation is: (P1 * V1) / T1 = (P2 * V2) / T2.

We are given the following initial conditions:

P1 = 1.50 atm

V1 = 3.50 L

T1 = 13.80 °C + 273.15 = 287.95 K (converted to Kelvin)

And the final conditions:

P2 = 0.993 atm

T2 = 22.00 °C + 273.15 = 295.15 K (converted to Kelvin)

We need to find V2, the final volume.

By substituting the given values into the combined gas law equation, we can calculate the final volume of the gas:

(1.50 atm * 3.50 L) / 287.95 K = (0.993 atm * V2) / 295.15 K

Solving for V2, we get:

V2 = (1.50 atm * 3.50 L * 295.15 K) / (0.993 atm * 287.95 K)

Therefore, the volume of the gas at 22.00 °C and 0.993 atm is approximately 5.03 L.