Question 5.3: A sample of CO2 gas has a volume of 575 cm³ at 752 torr and ......
A sample of CO_2 gas has a volume of 575 cm³ at 752 torr and 72°F. What is the mass of carbon dioxide in this sample?
Strategy We are trying to find the mass of a sample of gas. If we knew how many moles of CO_2 were in the sample, we could easily use the molar mass to find the mass of the sample. And since the problem involves a gas, we can attempt to use the ideal gas law to find the number of moles. We are given values for V, P, and T, so we will be able to solve for n. Some of the units given are unusual, so we will need to be careful to handle them properly.
We can begin by converting some of the given information into units more commonly used for gases.
T = (72 − 32) × 5/9 = 22°C = 295 K
V = 575 cm³ = 575 mL = 0.575 L
For P, we will use the value in torr and choose the corresponding value for R. We could also convert from torr to atm, of course.
n={\frac{P V}{R T}}={\frac{(752\ {\mathrm{torr}})(0.575\ {\mathrm{L}})}{(62.37\ {\mathrm{L}}\ {\mathrm{torr}}\ {\mathrm{mol}}^{-1}\ {\mathrm{K}}^{-1})(295\ {\mathrm{K}})}}=0.0235 mol
The gas in our sample is CO_2, with a molar mass of 44.0 g/mol, so
0.0235~\mathrm{mol}\times\frac{44.0~\mathrm{g}}{\mathrm{mol}}=1.03~\mathrm{g}~\mathrm{CO}_{2}
Analyze Your Answer The temperature and pressure are near typical room conditions, and the volume is a little more than a half liter. So this should correspond to a small balloon filled with CO_2. One gram is a pretty small mass but seems reasonable for the gas in a small balloon.
Check Your Understanding Find the volume in ft³ of 1.0 mole of an ideal gas at −25°C and 710 torr.