To find the partial pressure of CO2 and O2 gases, we need to calculate the pressure exerted by each gas individually.
Step 1: Calculate the mole fraction of CO2 and O2.
Mole fraction (X) is calculated by dividing the number of moles of a component by the total number of moles in the mixture. We are given the mole fraction for CO2 and O2.
Mole fraction of CO2 (X_CO2) = 0.0998
Mole fraction of O2 (X_O2) = 0.2340
Step 2: Calculate the number of moles of CO2 and O2.
We know that the sum of mole fractions equals 1.
X_CO2 + X_O2 = 1
Since X_CO2 is given as 0.0998, we can substitute this value and solve for X_O2.
0.0998 + X_O2 = 1
X_O2 = 1 - 0.0998
X_O2 = 0.9002
Now we can calculate the number of moles of each component using the mole fraction and the total pressure of the mixture.
Step 3: Calculate the number of moles.
PV = nRT
For CO2:
Partial pressure of CO2 (P_CO2) = X_CO2 * Total pressure
= 0.0998 * 0.6880 atm
For O2:
Partial pressure of O2 (P_O2) = X_O2 * Total pressure
= 0.9002 * 0.6880 atm
Step 4: Convert moles to pressure in atmospheres.
The ideal gas law gives us the equation PV = nRT.
We can rearrange this equation to solve for pressure.
Pressure (P) = n * R * T / V
Since we have the number of moles of each component, we can plug this into the equation to calculate the partial pressure of each gas.
Using the ideal gas constant R = 0.0821 L * atm / mol * K, and assuming temperature (T) and volume (V) are constant for both gases, we can calculate the partial pressures.
Step 5: Calculate pressure exerted by CO2 and O2.
Pressure (P) = n * R * T / V
Let's assume T and V are constants for both gases.
For CO2:
P_CO2 = (n_CO2 * R * T) / V
For O2:
P_O2 = (n_O2 * R * T) / V
Since the temperature and volume are the same for both gases, we can ignore those variables.
So, the partial pressure of CO2 is given by P_CO2 = (n_CO2 * R) / V
And the partial pressure of O2 is given by P_O2 = (n_O2 * R) / V
Now we can proceed with the calculation.
Step 6: Calculate the partial pressure of CO2 and O2.
P_CO2 = (n_CO2 * R) / V
= (0.0998 * 0.6880 atm) / (0.0821 L * atm / mol * K)
P_O2 = (n_O2 * R) / V
= (0.9002 * 0.6880 atm) / (0.0821 L * atm / mol * K)