Final answer:
To find the new volume of a gas when pressure is changed while temperature remains constant, you can use the combined gas law. Converting the initial pressure to the same unit as the final pressure, and using the formula P1V1 = P2V2, it was calculated that the volume would change to 8 liters when the pressure is increased to 5 atm.
Step-by-step explanation:
The student's question involves finding the new volume of a gas when the pressure is changed to 5 atm, given that the original volume was 40 L at 760 mmHg. To solve this, we use the combined gas law which states that P1V1/T1 = P2V2/T2, where P stands for pressure, V stands for volume, and T stands for temperature. In this question, the temperature is constant (not mentioned to change), so we simplify the formula to P1V1 = P2V2.
First, we must convert the pressures to the same unit. 760 mmHg is equivalent to 1 atm, so we have an initial pressure (P1) of 1 atm. The final pressure (P2) is 5 atm. The volume at 1 atm (V1) is 40 L. We are solving for the final volume (V2).
The steps are as follows:
- Write down the known variables: P1 = 1 atm, V1 = 40 L, P2 = 5 atm.
- Set up the equation P1V1 = P2V2.
- Plug in the known values and solve for V2: (1 atm * 40 L) = (5 atm * V2). This simplifies to V2 = (1 atm * 40 L) / 5 atm.
- Calculate the final volume: V2 = 40 L / 5 = 8 L.
Therefore, the new volume of the gas at 5 atm pressure would be 8 liters.