Question 8.3: When Whitney had her asthma attack, she was given oxygen thr...
When Whitney had her asthma attack, she was given oxygen through a face mask. The gauge on a 12-L tank of compressed oxygen reads 3800 mmHg. How many liters would this same gas occupy at a final pressure of 570 mmHg when temperature and amount of gas do not change?
STEP 1 State the given and needed quantities .We place the gas data in a table by writing the initial pressure and volume as P_{1} and V_{1} and the final pressure and volume as P_{2} and V_{2} . We see that the pressure decreases from 3800 mmHg to 570 mmHg.
Using Boyle’s law,
P_{1}V_{1}=P_{2}V_{2} No change in temperature and amount of gas (Boyle’s law)
we predict that the volume increases.
| ANALYZE THE PROBLEM | Given | Need | Connect |
| P_{1} = 3800 mmHg P_{2} = 570 mmHg V_{1} = 12 L
Factors that do not change: T and n |
\boxed{V_{2}} | Boyle’s law, P_{1}V_{1}=P_{2}V_{2}
Predict: P decreases, V increases |
STEP 2 Rearrange the gas law equation to solve for the unknown quantity.
For a PV relationship, we use Boyle’s law and solve for V_{2} by dividing both sides by P_{2}.
P_{1}V_{1}=P_{2} \boxed{V_{2}}\frac{P_{1}V_{1}}{P_{2}}=\frac{\cancel{P_{2}} \boxed{V_{2}}}{\cancel{P_{2}}}
\boxed{V_{2}} =V_{1} \times \frac{P_{1}}{P_{2}}
STEP 3 Substitute values into the gas law equation and calculate .When we substitute in the values with pressures in units of mmHg, the ratio of pressures (pressure factor) is greater than 1, which increases the volume as predicted.
\boxed{V_{2}} = 12 L \times \underset{\begin{array}{l}\text{Pressure factor}\\\text{increase volume}\end{array}}{\frac{3800 \cancel{mmHg}}{570 \cancel{mmHg}}} = 80. L