A sample of a smoke stack emission was collected into a 1.25L tank at 752 mm Hg and analyzed. The analysis showed 92% CO2, 3.6% NO, 1.2% SO2, and 4.1% H2O by mass. What is the partial pressure exerted by each gas?
To find the partial pressure exerted by each gas, we need to consider the composition of the sample and use the ideal gas law. The ideal gas law states that the pressure of a gas is directly proportional to the number of moles of the gas present.
First, let's calculate the number of moles of each gas in the sample. To do this, we'll assume that the total mass of the sample is 1 kg.
1. Calculate the mass of each gas in the sample:
- CO2: 92% of 1 kg = 0.92 kg
- NO: 3.6% of 1 kg = 0.036 kg
- SO2: 1.2% of 1 kg = 0.012 kg
- H2O: 4.1% of 1 kg = 0.041 kg
2. Convert the mass of each gas to moles using their molar masses:
- Molar mass of CO2 = 44 g/mol
Moles of CO2 = (0.92 kg / 44 g/mol) = 20.91 moles
- Molar mass of NO = 30 g/mol
Moles of NO = (0.036 kg / 30 g/mol) = 0.0012 moles
- Molar mass of SO2 = 64 g/mol
Moles of SO2 = (0.012 kg / 64 g/mol) = 0.00019 moles
- Molar mass of H2O = 18 g/mol
Moles of H2O = (0.041 kg / 18 g/mol) = 0.0023 moles
Now that we have the number of moles of each gas, we can calculate the partial pressure exerted by each gas using the ideal gas law equation: P = nRT/V.
In this case, we have the volume (V) of the sample (1.25 L) and the total pressure (P) exerted by the gas mixture (752 mm Hg). We'll assume the temperature (T) is constant.
3. Calculate the partial pressure of each gas:
- Partial pressure of CO2 (P(CO2)):
P(CO2) = (n(CO2) * R * T) / V
- Partial pressure of NO (P(NO)):
P(NO) = (n(NO) * R * T) / V
- Partial pressure of SO2 (P(SO2)):
P(SO2) = (n(SO2) * R * T) / V
- Partial pressure of H2O (P(H2O)):
P(H2O) = (n(H2O) * R * T) / V
Note: The gas constant (R) is 0.0821 L.atm/mol.K.
4. Plug in the values and calculate the partial pressures:
- P(CO2) = (20.91 moles * 0.0821 L.atm/mol.K * T) / 1.25 L
- P(NO) = (0.0012 moles * 0.0821 L.atm/mol.K * T) / 1.25 L
- P(SO2) = (0.00019 moles * 0.0821 L.atm/mol.K * T) / 1.25 L
- P(H2O) = (0.0023 moles * 0.0821 L.atm/mol.K * T) / 1.25 L
5. Since the temperature (T) is not given in the question, we cannot calculate the exact partial pressures. However, we can calculate the values relative to each other by assuming a constant temperature. For example, if the temperature is 298 K (25°C), you can calculate:
- P(CO2) = (20.91 * 0.0821 * 298) / 1.25 (unit: atm)
- P(NO) = (0.0012 * 0.0821 * 298) / 1.25 (unit: atm)
- P(SO2) = (0.00019 * 0.0821 * 298) / 1.25 (unit: atm)
- P(H2O) = (0.0023 * 0.0821 * 298) / 1.25 (unit: atm)
By substituting the values for P(CO2), P(NO), P(SO2), and P(H2O), you can calculate the partial pressure exerted by each gas.