Calculate to three significant digits the density of carbon dioxide gas at exactly 20°C and exactly 1atm. You can assume carbon dioxide gas behaves as an ideal gas under these conditions.
Question
Calculate to three significant digits the density of carbon dioxide gas at exactly 20°C and exactly 1atm. You can assume carbon dioxide gas behaves as an ideal gas under these conditions.
Solution
To calculate the density of carbon dioxide gas at exactly 20°C and exactly 1atm, we can use the ideal gas law, which is PV = nRT.
Step 1: Convert the temperature to Kelvin. The Kelvin scale starts at absolute zero, which is -273.15°C. So, 20°C is 20 + 273.15 = 293.15 K.
Step 2: Rearrange the ideal gas law to solve for n/V, which is the number of moles per volume, or the density. The rearranged formula is n/V = P/RT.
Step 3: Plug in the values. The pressure P is 1 atm, the gas constant R is 0.0821 L·atm/(K·mol), and the temperature T is 293.15 K. So, n/V = 1 atm / (0.0821 L·atm/(K·mol) * 293.15 K) = 0.0446 mol/L.
Step 4: Convert the molar mass of CO2 from grams per mole to kilograms per mole. The molar mass of CO2 is approximately 44.01 g/mol, which is 0.04401 kg/mol.
Step 5: Multiply the molar density by the molar mass to get the mass density. So, the density of CO2 is 0.0446 mol/L * 0.04401 kg/mol = 0.00196 kg/L.
Step 6: Round to three significant digits. The density of CO2 at 20°C and 1 atm is approximately 0.00196 kg/L, or 1.96 kg/m^3 to three significant digits.
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