Question 10.2.1: Use Boyle’s law to calculate volume. A sample of gas has a v......
Use Boyle’s law to calculate volume.
A sample of gas has a volume of 458 mL at a pressure of 0.970 atm. The gas is compressed and now has a pressure of 3.20 atm. Predict if the new volume is greater or less than the initial volume, and calculate the new volume. Assume temperature is constant and no gasescaped from the container.
You are asked to calculate the volume of a gas sample when only the pressure is changed.
You are given the original volume and pressure and the new pressure of the gas sample.
According to Boyle’s law, pressure and volume are inversely related when the temperature and amount of gas are held constant. In this case, the pressure increases from 0.970 atm to 3.20 atm, so the new volume should decrease. It will be less than the original volume.
To calculate the new volume, first make a table of the known and unknown pressure and volume data. In this case, the initial volume and pressure and the new pressure are known and the new volume must be calculated.
P_{1} = 0.970 atm P_{2} = 3.20 atm
V_{1} = 458 mL V_{2} = ?
Rearrange Boyle’s law to solve for V_{2} and calculate the new volume of the gas sample.
P_{1}V_{1}= P_{2}V_{2}
V_{2} = \frac{P_{1}V_{1}}{P_{2}} =\frac{\left(0.970\text{ atm}\right) \left(458\text{ mL}\right) }{3.20\text{ atm}} = 139 mL
The pressure units (atm) cancel, leaving volume in units of milliliters.
Is your answer reasonable? The final volume is less than the initial volume, as we predicted.