Answered

At 700.°C, the total pressure of the system is found to be 3.01 atm. If the equilibrium constant KP is 1.52, calculate the equilibrium partial pressures of CO2 and CO.

Answer :

Answer:

Pco = 1.51 atm

Pco[tex]_{2}[/tex] = 1.5 atm

Explanation:

C (s) + CO2 (g) 2 CO (g)

T = 700°C, P (total) = 3.01 atm, KP = 1.52

Mathematically,

KP = [tex]\frac{(Pco)^{2} }{Pco_{2} }[/tex]

According to Dalton' Law which states that at equilibrium, the sum of the partial pressures of each component is equal to the total pressure

Mathematically,

P (total) = Pco[tex]_{2}[/tex] + Pco = 3.01 atm

Pco[tex]_{2}[/tex] = P (total) - Pco

Pco[tex]_{2}[/tex] = 3.01 - Pco

Substitute Pco[tex]_{2}[/tex] into the KP equation, we have

KP = [tex]\frac{(Pco)^{2} }{3.01 - Pco }[/tex] ⇒ 1.52 = [tex]\frac{(Pco)^{2} }{3.01 - Pco }[/tex]

Let y = Pco

1.52 = [tex]\frac{(y)^{2} }{3.01 - y }[/tex] = [tex]y^{2}[/tex] = 1.52 (3.01 - y)

[tex]y^{2}[/tex] = 4.5752 - 1.52y ⇒  [tex]y^{2}[/tex] + 1.52y - 4.5752 = 0

Using the quadratic formula y = [tex]\frac{-b + \sqrt{b^{2} -4ac } }{2a}[/tex] and y = [tex]\frac{-b - \sqrt{b^{2} -4ac } }{2a}[/tex]

y = 1.51 or −3.03

We choose the positive root because Pco cannot be negative (Remember Pco = y)

Hence, Pco = 1.51 atm

Pco[tex]_{2}[/tex] = 3.01 - Pco = 3.01 - 1.51

Pco[tex]_{2}[/tex] = 1.5 atm