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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