How Do You Calculate the Original Volume of Gas After Pressure Change?

[hecate]

can anyone tell me the steps to do this problem?

You are given a gas that you measure under a pressure of 720 mmHg. When the pressure is changed to 760 mmHg, the volume becomes 580 mL. What was the original volume of the gas?

I don't know how to do this problem. thanx!

 

[Warr]

Its this simple ratio:

\frac{P_{1}}{V_{1}} = \frac{P_{2}}{V_{2}}

so to find V_{1}

V_{1} = \frac {P_{1}V_{2}}{P_{2}}

 

[M98Ranger]

Sure, I'd be happy to help you with this problem! Here are the steps to solve it:

1. Write down the given information: pressure 1 (P1) = 720 mmHg, pressure 2 (P2) = 760 mmHg, volume 2 (V2) = 580 mL.

2. Use the combined gas law formula: P1V1/T1 = P2V2/T2, where P1 and P2 are the pressures, V1 and V2 are the volumes, and T1 and T2 are the temperatures.

3. Since the temperature is constant in this problem, we can remove it from the equation. This leaves us with P1V1 = P2V2.

4. Plug in the given values: (720 mmHg)(V1) = (760 mmHg)(580 mL).

5. Solve for V1 by dividing both sides by 720 mmHg: V1 = (760 mmHg)(580 mL) / 720 mmHg.

6. Use unit conversion to convert mmHg to mL: 1 mmHg = 1 mL, so the units cancel out and we are left with V1 = 760 mL.

7. Therefore, the original volume of the gas was 760 mL. I hope this helps! Let me know if you have any other questions.