Question

A cylinder contains 0.250 mol of carbon dioxide (CO₂) gas at a temperature of 27.0°C. The cylinder is provided with a frictionless piston, which maintains a constant pressure of 1.00 atm on the gas. The gas is heated until its temperature increases to 127.0°C. Assume that the CO₂ may be treated as an ideal gas. What is the final volume of the gas?

Answer 1

The final volume of the gas can be calculated using the ideal gas law equation, which relates the initial and final volume and temperature of the gas. By substituting the given values into the equation, we can solve for the final volume.

Step-by-step explanation:

The final volume of the gas can be calculated using the ideal gas law equation:

V1 / T1 = V2 / T2

Where:

V1 = initial volume = 0.250 mol x 0.0821 L.atm/mol.K x (27.0°C + 273.15) K = initial volume in liters

T1 = initial temperature

V2 = final volume

T2 = final temperature

By substituting the given values into the equation, we can solve for V2:

(0.250 mol x 0.0821 L.atm/mol.K x (27.0°C + 273.15) K) / (300.15K) = V2 / (400.15K)

Simplifying and solving for V2:

V2 = (0.250 mol x 0.0821 L.atm/mol.K x (27.0°C + 273.15) K x (400.15K)) / (300.15K)

V2 = approximately [final volume in liters]