Carbon monoxide and chlorine gas react to form phosgene. If a reaction mixture initially contains 215 torr of CO and 245 torr of Cl₂. 0.76 is the mole fraction of COCl₂ when equilibrium is reached.
CO(g) + Cl₂ (g) → COCl₂ (g) Kp = 310
With this reaction we can write the Kp expression
[tex]K_{p} = \frac{p_{COCl_2}}{p_{CO} \times p_{Cl_2}}[/tex]
We know that 1 atm = 760 torr
Now
[tex]p_{CO} = \frac{215 \times 1}{760}[/tex]
= 0.28 atm
[tex]p_{Cl_2} = \frac{245 \times 1}{760}[/tex]
= 0.32 atm
Now, we can write an ICE chart with pressures, so we can know the pressure of COCl₂.
CO(g) + Cl₂ (g) → COCl₂ (g) Kp = 310
I: 0.28 0.32 0
C: -x -x +x
E: 0.28 - x 0.32 - x x
Now put the value in Kp expression
[tex]K_{p} = \frac{p_{COCl_2}}{p_{CO} \times p_{Cl_2}}[/tex]
[tex]310 = \frac{x}{(0.28 - x) (0.32 - x)}[/tex]
[tex]310 = \frac{x}{0.0896 - 0.28x - 0.32x + x^2}[/tex]
310 (0.0896 - 0.28x - 0.32x + x²) = x
310 (0.0896 - 0.6 x + x²) = x
27.776 - 186 x + 310 x² = x
310 x² -187 x + 27.776 = 0
By using the quadratic equation find the value of x:
[tex]x = \frac{b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]= \frac{187 \pm \sqrt{(187)^2 - 4 \times 310 \times 27.776}}{2 \times 310}[/tex]
[tex]= \frac{187 \pm \sqrt{34969 - 34,442.24}}{620}[/tex]
[tex]= \frac{187 \pm \sqrt{526.76}}{620}[/tex]
[tex]= \frac{187 \pm 22.95}{620}[/tex]
[tex]= \frac{187 + 22.95}{620}\ \text{or}\ \frac{187 - 22.95}{620}[/tex]
[tex]= \frac{209.95}{620}\ \text{or}\ \frac{164.05}{620}[/tex]
[tex]= 0.33\ \text{or}\ 0.26[/tex]
Using the lowest value of x, we have that the partial pressure of COCl₂ would be 0.26 atm.
PpCO = 0.28 - x = 0.28 - 0.26 = 0.02
PpCl₂ = 0.32 - x = 0.32 - 0.26 = 0.06
[tex]X_{COCl_2} = \frac{P_{COCl_2}}{Pt}[/tex]
And Pt is the total pressure of all species in reaction so:
Pt = 0.02 + 0.06 + 0.26 =
= 0.34 atm
The mole fraction:
[tex]X_{COCl_2} = \frac{0.26}{0.34}[/tex]
= 0.76
Thus from the above conclusion we can say that Carbon monoxide and chlorine gas react to form phosgene. If a reaction mixture initially contains 215 torr of CO and 245 torr of Cl₂. 0.76 is the mole fraction of COCl₂ when equilibrium is reached.
Learn more about the Mole Fraction here: https://brainly.com/question/14498215
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