Answer:
K = 6.5 × 10⁻⁶
Explanation:
C₅H₆O₃(g) → C₂H₆(g) + 3 CO(g)
The formula for the ideal gas law
PV = nRT
where
P = total pressure
V = volume
n = total moles
R = gas constant
T = absolute temperature
P(C₅H₆O₃) = nRT/V
where
n = 5.63 /114
= 0.049
[tex]= \frac{0.049 * 0.0821 * 473}{2.5}[/tex]
= [tex]0.78atm[/tex]
C₅H₆O₃(g) ⇄ C₂H₆(g) + 3 CO(g)
0.78atm 0 0
0.78 - x x 3x
P(total) = 1.63atm
0.78atm - x + x + 3x⇒x = 0.288atm
P(C₅H₆O₃) = 0.78 - 0.288
= 0.489 atm
P(C₂H₆) = 0.288 atm
P(CO) = 0.846 atm
[tex]Kp = \frac{0.288 * 0.864^3}{0.489}[/tex]
= 0.379
K = Kp/(RT³)
[tex]= \frac{0.379}{(0.0821 * 473)^3} \\= 6.5 * 10^-^6[/tex]
K = 6.5 × 10⁻⁶
The value of K for this reaction is : 6.5 * 10⁻⁶
The decomposition equation
C₅H₆O₃ ----> C₂H₆ (g) + 3 CO (g)
Given data :
mass of pure C₅H₆O₃ = 5.63 g
volume of flask = 2.50 L
Temperature = 200°C = 473 K
Pressure in flask = 1.63 atm
we will apply Ideal gas law formula
PV = nRT
therefore P( C₅H₆O₃ ) = nRT / V ---- ( 1 )
where : n = 5.63 / 114 = 0.049, V = 2.5 L, R = 0.0821, T = 473 k
Insert values into equation ( 1 )
P( C₅H₆O₃ ) = 0.78 atm - x ---- ( 2 )
P(total) = 1.63 atm.
Considering the decomposition equation
0.78 - x + x + 3x = 1.63 atm
therefore ; x = 0.288
back to equation ( 2 )
P( C₅H₆O₃ ) = 0.78 - 0.288 = 0.489 atm
Given that :
P(C₂H₆) = 0.288 atm
P(CO) = 0.846 atm
Find K using the relationship below
K = Kp / ( RT)³ ------ ( 3 )
While Kp = ( 0.288 * 0.864³ ) / 0.489
= 0.379
Back to equation ( 3 )
K = 0.379 / ( 0.0821 * 473 )³
= 6.5 × 10⁻⁶.
Hence we can conclude that the value of K for this reaction is : 6.5 * 10⁻⁶
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