Final answer:
To determine the mass of CO₂ in a sample given its volume, temperature, and pressure, one must use the ideal gas law to solve for the number of moles and then multiply by the molar mass of CO₂.
Step-by-step explanation:
A student asks how many grams of carbon dioxide (CO₂) are in a sample that has a volume of 26.5 mL at 20 degrees Celsius and 624 torr. To answer this question, we need to use the ideal gas law, which is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvins.
First, we must convert the given volume from mL to liters and the pressure from torr to atmospheres, and the temperature to Kelvins. Then we solve for n, the number of moles, using R (0.0821 L·atm/K·mol). Finally, by multiplying the number of moles by the molar mass of CO₂ (44.01 g/mol), we find the mass in grams.
Here is a breakdown of the steps:
- Convert 26.5 mL to 0.0265 L.
- Convert 624 torr to 0.8205 atm (using the conversion 1 atm = 760 torr).
- Convert 20°C to 293 K (by adding 273 to the Celsius temperature).
- Use the ideal gas law to solve for n (n = PV/RT).
- Calculate the mass of CO₂ using the molar mass.
This calculation will give the mass of CO₂ in the sample in grams.