Question

Carbon monoxide and chlorine gas react to form phosgene:

Answer 1

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.

How to find Mole fraction ?

CO(g) + Cl₂ (g) → COCl₂ (g)           Kp = 310

With this reaction we can write the Kp expression

$K_{p} = \frac{p_{COCl_2}}{p_{CO} \times p_{Cl_2}}$

We know that 1 atm = 760 torr

Now

$p_{CO} = \frac{215 \times 1}{760}$

       = 0.28 atm

$p_{Cl_2} = \frac{245 \times 1}{760}$

        = 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

$K_{p} = \frac{p_{COCl_2}}{p_{CO} \times p_{Cl_2}}$

$310 = \frac{x}{(0.28 - x) (0.32 - x)}$

$310 = \frac{x}{0.0896 - 0.28x - 0.32x + x^2}$

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:

$x = \frac{b \pm \sqrt{b^2 - 4ac}}{2a}$

  $= \frac{187 \pm \sqrt{(187)^2 - 4 \times 310 \times 27.776}}{2 \times 310}$

  $= \frac{187 \pm \sqrt{34969 - 34,442.24}}{620}$

  $= \frac{187 \pm \sqrt{526.76}}{620}$

  $= \frac{187 \pm 22.95}{620}$

  $= \frac{187 + 22.95}{620}\ \text{or}\ \frac{187 - 22.95}{620}$

  $= \frac{209.95}{620}\ \text{or}\ \frac{164.05}{620}$

  $= 0.33\ \text{or}\ 0.26$

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

$X_{COCl_2} = \frac{P_{COCl_2}}{Pt}$

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:

$X_{COCl_2} = \frac{0.26}{0.34}$

             = 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

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