Can I get detailed answer for this one Thanks Explain what i

Can I get detailed answer for this one? Thanks

Explain what is meant by the partial pressure of a component in a mixture of gases. Show that, for a mixture of Ideal Gases, the mol fraction of a component of the mixture is equal to the partial pressure of that component divided by the total pressure of the mixture. Natural gas (CH4) is burned at atmospheric pressure, at an air:fuel ratio (AFR) of 20:1 Treating the combustion products as a mixture of Ideal Gases, calculate the partial pressure of CO_2 in the exhaust gases. Briefly explain the role and operating principle of a three-way catalytic converter (TWC) in the exhaust system of a spark-ignition engine.

Solution

a) Partial pressure: The pressure due to any individual component in a gas mixture is its partial pressure. We can calculate partial pressure from the ideal gas law by assuming that each gas component acts independently.

Example: A mixture containing 5.2 g each of CH4(g), C2H4(g) and C4H10(g) is contained in a 1.50 L flask at a temperature of 25°C. Calculate the partial pressure of each of the gases in the mixture.

Ans:  First, the number of moles of each gas is calculated:
CH4 = 5.2 g / 16 g/ mol = 0.325 mol
C2H4 = 5.2 g / 28 g/ mol = 0.186 mol
C4H10 = 5.2 g / 58 g/ mol = 0.089 mol

Second, the pressure of each gas is calculated by using ideal gas law.
V = 1.50 L
T = 25°C = 298 K
R = 0.082 atm.L/mol.K

P = nRT/V

CH4 => P = (0.325)(0.082)(298) / (1.5) = 5.29 atm
C2H4 => P = (0.186)(0.082)(298) / (1.5) = 3.03 atm
C4H10 => P = (0.089)(0.082)(298) / (1.5) = 1.45 atm

Dalton\'s Law (also called Dalton\'s Law of Partial Pressures) states that the total pressure exerted by the mixture of non-reactive gases is equal to the sum of the partial pressures of individual gases.

For a multicomponent gas mixture, we calculate the partial pressure of each component from the ideal gas law and the number of moles of that component ( n_n ) as follows:

P_a = n_aRT/V ; P_b= n_bRT/V ; P_c= n_cRT/V ;

The sum of the partial pressures of the components in a gas mixture equals the total pressure:

P_total = P_a + P_b + P_c

b) Mole fraction: The number of moles of a component in a mixture divided by the total number of moles in the mixture, is the mole fraction.

x_a = n_a/n_total --------------------- (1)

where, x_a = mole fraction; n_a = moles of a component in a mixture; n_total = total number of moles in the mixture

Now, P_a/P_total = (n_aRT/V)/(n_totalRT/V) =  n_a/n_total --------------------- (2)

Where, P_a = partial pressure from contribution of a single gas; P_total = total pressure of the mixture

Hence, from equation (1) and (2), it is proved that ,mole fraction of a omponent of the mixture is equal to the partial pressure of that component devided by total pressure of the mixture.