Consider the following reaction: 2SO2(g)+O2(g)⇌2SO3(g) Kp=0.355 at 950 K A 2.75−L reaction vessel at 950K initially contains 0.100 mol of SO2 and 0.100 mol of O2.Calculate the total pressure (in atmospheres) in the reaction vessel when equilibrium is reached.

Respuesta :

Answer : The total pressure (in atmospheres) in the reaction vessel when equilibrium reached is, 5.02 atm

Explanation :

First we have to calculate the initial pressure of [tex]SO_2[/tex] and [tex]O_2[/tex]

[tex]P_{SO_2}=\frac{n_{SO_2}RT}{V}[/tex]

[tex]P_{SO_2}=\frac{(0.100mol)\times (0.0821L.atm/mol.K)\times (950K)}{2.75L}[/tex]

[tex]P_{SO_2}=2.84atm[/tex]

and,

[tex]P_{O_2}=\frac{n_{O_2}RT}{V}[/tex]

[tex]P_{O_2}=\frac{(0.100mol)\times (0.0821L.atm/mol.K)\times (950K)}{2.75L}[/tex]

[tex]P_{O_2}=2.84atm[/tex]

The balanced chemical reaction is:

                             [tex]2SO_2(g)+O_2(g)\rightleftharpoons 2SO_3(g)[/tex]

Initial pressure     2.84        2.84           0

At eqm.              (2.84-2x)  (2.84-x)        2x

The expression of [tex]K_p[/tex] for above reaction follows:

[tex]K_p=\frac{(P_{SO_3})^2}{(P_{SO_2})^2\times P_{O_2}}[/tex]

Putting values in expression 1, we get:

[tex]0.355=\frac{(2x)^2}{(2.84-2x)^2\times (2.84-x)}[/tex]

x = 0.664

Now we have to calculate the total pressure.

Partial pressure of [tex]SO_3[/tex] = (2x) = 2(0.664) = 1.33 atm

Partial pressure of [tex]SO_2[/tex] = (2.84-2x) = [2.84-2(0.664)] = 1.51 atm

Partial pressure of [tex]O_2[/tex] = (2.84-x) = [2.84-0.664] = 2.18 atm

Total pressure = Partial pressure of [tex]SO_3[/tex] + Partial pressure of [tex]SO_2[/tex] + Partial pressure of [tex]O_2[/tex]

Total pressure = 1.33 + 1.51 + 2.18

Total pressure = 5.02 atm

Thus, the total pressure (in atmospheres) in the reaction vessel when equilibrium reached is, 5.02 atm

The total pressure  is mathematically given as

T=5.02

What is the total pressure in the reaction vessel?

Generally, the equation for the pressure  is mathematically given as

For SO2

[tex]P_{SO_2}=\frac{n_{SO_2}RT}{V}[/tex]

Therefore

[tex]P_{SO_2}=\frac{(0.100)* (0.0821)* (950K)}{2.75L}[/tex]

[tex]P_{SO_2}=2.84atm[/tex]

For O2

[tex]P_{O_2}=\frac{(0.100)* (0.0821)* (950K)}{2.75L}\\\\P_{O_2}=2.84atm[/tex]

Hence, The balanced equation is

2SO_2(g)+O_2(g)  ---><---- 2SO_3(g)

Therefore using Kp equation

[tex]0.355=\frac{(2x)^2}{(2.84-2x)^2* (2.84-x)}[/tex]

x=0.67

Now solving partial pressure for SO3,SO2,O2 We have

PSO3= (2x) = 2(0.664)

PSO3= 1.33 atm

PSO2 = (2.84-2x)

PSO2 = 1.51 atm

PO=  [2.84-0.664]

PO= 2.18 atm

Tottal pressure

T=1.33 + 1.51 + 2.18

T=5.02

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