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.
<h3>How to find Mole fraction ? </h3>
CO(g) + Cl₂ (g) → COCl₂ (g) Kp = 310
With this reaction we can write the Kp expression
![K_{p} = \frac{p_{COCl_2}}{p_{CO} \times p_{Cl_2}}](https://tex.z-dn.net/?f=K_%7Bp%7D%20%3D%20%5Cfrac%7Bp_%7BCOCl_2%7D%7D%7Bp_%7BCO%7D%20%5Ctimes%20p_%7BCl_2%7D%7D)
We know that 1 atm = 760 torr
Now
= 0.28 atm
![p_{Cl_2} = \frac{245 \times 1}{760}](https://tex.z-dn.net/?f=p_%7BCl_2%7D%20%3D%20%5Cfrac%7B245%20%5Ctimes%201%7D%7B760%7D)
= 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
![K_{p} = \frac{p_{COCl_2}}{p_{CO} \times p_{Cl_2}}](https://tex.z-dn.net/?f=K_%7Bp%7D%20%3D%20%5Cfrac%7Bp_%7BCOCl_2%7D%7D%7Bp_%7BCO%7D%20%5Ctimes%20p_%7BCl_2%7D%7D)
![310 = \frac{x}{(0.28 - x) (0.32 - x)}](https://tex.z-dn.net/?f=310%20%3D%20%5Cfrac%7Bx%7D%7B%280.28%20-%20x%29%20%280.32%20-%20x%29%7D)
![310 = \frac{x}{0.0896 - 0.28x - 0.32x + x^2}](https://tex.z-dn.net/?f=310%20%3D%20%5Cfrac%7Bx%7D%7B0.0896%20-%200.28x%20-%200.32x%20%2B%20x%5E2%7D)
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:
![x = \frac{b \pm \sqrt{b^2 - 4ac}}{2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7Bb%20%5Cpm%20%5Csqrt%7Bb%5E2%20-%204ac%7D%7D%7B2a%7D)
![= \frac{187 \pm \sqrt{(187)^2 - 4 \times 310 \times 27.776}}{2 \times 310}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B187%20%5Cpm%20%5Csqrt%7B%28187%29%5E2%20-%204%20%5Ctimes%20310%20%5Ctimes%2027.776%7D%7D%7B2%20%5Ctimes%20310%7D)
![= \frac{187 \pm \sqrt{34969 - 34,442.24}}{620}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B187%20%5Cpm%20%5Csqrt%7B34969%20-%2034%2C442.24%7D%7D%7B620%7D)
![= \frac{187 \pm \sqrt{526.76}}{620}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B187%20%5Cpm%20%5Csqrt%7B526.76%7D%7D%7B620%7D)
![= \frac{187 \pm 22.95}{620}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B187%20%5Cpm%2022.95%7D%7B620%7D)
![= \frac{187 + 22.95}{620}\ \text{or}\ \frac{187 - 22.95}{620}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B187%20%2B%2022.95%7D%7B620%7D%5C%20%5Ctext%7Bor%7D%5C%20%5Cfrac%7B187%20-%2022.95%7D%7B620%7D)
![= \frac{209.95}{620}\ \text{or}\ \frac{164.05}{620}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B209.95%7D%7B620%7D%5C%20%5Ctext%7Bor%7D%5C%20%5Cfrac%7B164.05%7D%7B620%7D)
![= 0.33\ \text{or}\ 0.26](https://tex.z-dn.net/?f=%3D%200.33%5C%20%5Ctext%7Bor%7D%5C%200.26)
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
![X_{COCl_2} = \frac{P_{COCl_2}}{Pt}](https://tex.z-dn.net/?f=X_%7BCOCl_2%7D%20%3D%20%5Cfrac%7BP_%7BCOCl_2%7D%7D%7BPt%7D)
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:
![X_{COCl_2} = \frac{0.26}{0.34}](https://tex.z-dn.net/?f=X_%7BCOCl_2%7D%20%3D%20%5Cfrac%7B0.26%7D%7B0.34%7D)
= 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: brainly.com/question/14498215
#SPJ1