2NO(g) + O2(g) = 2NO2
If there are .02 moles of O2, .04 moles of NO, and .96 moles of 2NO2, calculate Kp if the total pressure is .2 atm.
The partial pressures are:
(0.02/1.02) * 0.2 = 0.00392 atm O2
(0.04/1.02) * 0.2 = 0.00784 atm NO
(0.96/1.02) * 0.2 = 0.1882 atm NO2
Now calculate the appropriate Kp value.
Kp = PCO2^2/[PNO^2*PO2]
This assumes that mixture is in chemical equlibrium. This is not always the case.
To calculate the equilibrium constant (Kp) for the given reaction, we need to write the balanced equation and determine the partial pressures of the gases at equilibrium.
The balanced equation for the reaction is:
2 NO(g) + O2(g) ↔ 2 NO2(g)
Let's assume that the initial pressure of O2 is P(O2), the initial pressure of NO is P(NO), and the initial pressure of NO2 is P(NO2).
At equilibrium, the partial pressure of each gas can be expressed as:
P(O2) = (.2 - P(NO2)) (from the given total pressure of 0.2 atm)
P(NO) = (.2 - P(NO2))/2 (since the stoichiometric coefficient of NO is 0.5 in the balanced equation)
P(NO2) = P(NO2) (since the pressure term does not change for NO2)
Using the given moles of each gas and the ideal gas law equation (PV = nRT), we can calculate the initial mole fraction (X) of each gas:
X(NO2) = (0.96 moles of NO2) / (1 mole of NO2 + 0.04 moles of NO + 0.02 moles of O2 + 0.96 moles of NO2)
X(NO) = (0.04 moles of NO) / (1 mole of NO2 + 0.04 moles of NO + 0.02 moles of O2 + 0.96 moles of NO2)
X(O2) = (0.02 moles of O2) / (1 mole of NO2 + 0.04 moles of NO + 0.02 moles of O2 + 0.96 moles of NO2)
Using the mole fractions, we can express the partial pressures at equilibrium in terms of X:
P(NO2) = X(NO2) * (.2 - P(NO2))
P(NO) = X(NO) * (.2 - P(NO2))/2
P(O2) = X(O2) * (.2 - P(NO2))
Now, let's solve for P(NO2) in terms of X(NO2):
P(NO2) = X(NO2) * (.2 - P(NO2))
P(NO2) = X(NO2) * .2 - X(NO2)*P(NO2)
P(NO2) + X(NO2)*P(NO2) = X(NO2) * .2
P(NO2) * (1 + X(NO2)) = X(NO2) * .2
P(NO2) = (X(NO2) * .2) / (1 + X(NO2))
Substituting P(NO2) back into the expressions for P(NO) and P(O2), we have:
P(NO) = X(NO) * (.2 - [(X(NO2) * .2) / (1 + X(NO2))])/2
P(O2) = X(O2) * (.2 - [(X(NO2) * .2) / (1 + X(NO2))])
Finally, since Kp is calculated using the partial pressures raised to the power of their stoichiometric coefficients, we have:
Kp = (P(NO2))^2 / (P(NO))^2 * (P(O2))
Substituting the expressions we derived earlier into the equation for Kp, we have:
Kp = ([X(NO2) * .2 / (1 + X(NO2))])^2 / ([X(NO) * (.2 - X(NO2) * .2 / (1 + X(NO2))) / 2])^2 * ([X(O2) * (.2 - X(NO2) * .2 / (1 + X(NO2)))])
Note that calculating the exact value of Kp requires knowing the value of the mole fractions X(NO2), X(NO), and X(O2). You can substitute the given values of .02 moles of O2, .04 moles of NO, and .96 moles of NO2 into the equations to get the mole fractions and then calculate the value of Kp.