A sample of a smoke stack emission was collected into a 1.25 L 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 first calculate the mole fraction of each gas in the mixture.
Mole fraction (X) is the ratio of the number of moles of a component to the total number of moles in the mixture. It is calculated using the mass fraction (w) and the molar mass (M) of each component:
X = (w/M) / Σ (w/M)
Let's calculate the mole fraction for each gas:
For CO2:
Molar mass (M) of CO2 = 44.01 g/mol
Mass fraction (w) of CO2 = 92% = 0.92
X(CO2) = (w/M) / Σ (w/M) = (0.92/44.01) / [(0.92/44.01) + (0.036/30.0) + (0.012/64.0) + (0.041/18.02)]
Similarly, calculate the mole fraction for NO, SO2, and H2O using their respective molar masses and mass fractions.
Once we have the mole fraction for each gas, we can use Dalton's law of partial pressures to calculate the partial pressure exerted by each gas.
According to Dalton's law, the total pressure exerted by a mixture of gases is the sum of the partial pressures of the individual gases. The partial pressure of each gas is calculated by multiplying the mole fraction of the gas by the total pressure.
Let's calculate the partial pressure exerted by each gas:
Partial pressure of CO2 = X(CO2) * Total pressure
Partial pressure of NO = X(NO) * Total pressure
Partial pressure of SO2 = X(SO2) * Total pressure
Partial pressure of H2O = X(H2O) * Total pressure
Substituting the calculated mole fractions and the given total pressure (752 mm Hg), we can find the partial pressure exerted by each gas.
Each is done the same way. For CO2,
X CO2 is 0.92, then
pCO2 = XCO2*Ptotal