Question

In an experiment, 25.0 mL of a gas with a pressure of 1.00 atm is contained in a balloon at 25°C. The balloon is then cooled to 5°C and the pressure is found to be 0.750 atm. What is the volume of the gas under the new conditions?

A. 0.90 mL
B. 1.2 mL
C. 73 mL
D. 263 mL
E. 31 mL

Answer 1

E. 31 mL. The volume of the gas under the new conditions of 0.750 atm pressure and 5°C temperature is found to be 31 mL, using the combined gas law.

Step-by-step explanation:

The student's question pertains to the application of the combined gas law to determine the new volume of a gas when it is subjected to a change in temperature and pressure. Given the initial conditions of 25.0 mL of gas at a pressure of 1.00 atm and a temperature of 25°C, and the final conditions being a temperature of 5°C and a pressure of 0.750 atm, we are to find the final volume.

The combined gas law is P1V1/T1 = P2V2/T2, where P is the pressure, V is the volume, and T is the temperature in Kelvin. We can rearrange this equation to solve for V2: V2 = (P1V1T2)/(P2T1).

To solve the problem, convert the temperatures to Kelvin by adding 273.15 to the Celsius values. This gives us T1 = 298.15 K and T2 = 278.15 K.

Now, using the combined gas law: V2 = (1.00 atm × 25.0 mL × 278.15 K) / (0.750 atm × 298.15 K) = 31 mL, which corresponds to option (E).