Answer :
(a) The value of
is, ![5.0\times 10^{-4}](https://tex.z-dn.net/?f=5.0%5Ctimes%2010%5E%7B-4%7D)
(b) The value of
is, ![3.83\times 10^{-2}](https://tex.z-dn.net/?f=3.83%5Ctimes%2010%5E%7B-2%7D)
Explanation:
(a) We have to determine the value of
.
The given balanced reaction is,
![2A(g)+2B(g)\rightleftharpoons C(g)](https://tex.z-dn.net/?f=2A%28g%29%2B2B%28g%29%5Crightleftharpoons%20C%28g%29)
The relation between
and
are :
![K_p=K_c\times (RT)^{\Delta n}](https://tex.z-dn.net/?f=K_p%3DK_c%5Ctimes%20%28RT%29%5E%7B%5CDelta%20n%7D)
where,
= equilibrium constant at constant pressure = ?
= equilibrium concentration constant = 55.6
R = gas constant = 0.08206 L⋅atm/(K⋅mol)
T = temperature = ![313^oC=273+313=586K](https://tex.z-dn.net/?f=313%5EoC%3D273%2B313%3D586K)
= change in the number of moles of gas = [1 - (2 + 2)] = -3
Now put all the given values in the above relation, we get:
![K_p=55.6\times (0.08206L.atm/K.mol\times 586K)^{-3}](https://tex.z-dn.net/?f=K_p%3D55.6%5Ctimes%20%280.08206L.atm%2FK.mol%5Ctimes%20586K%29%5E%7B-3%7D)
![K_p=0.00050=5.0\times 10^{-4}](https://tex.z-dn.net/?f=K_p%3D0.00050%3D5.0%5Ctimes%2010%5E%7B-4%7D)
The value of
is, ![5.0\times 10^{-4}](https://tex.z-dn.net/?f=5.0%5Ctimes%2010%5E%7B-4%7D)
(b) We have to determine the value of
.
The given balanced reaction is,
![X(g)+2Y(g)\rightleftharpoons 3Z(g)](https://tex.z-dn.net/?f=X%28g%29%2B2Y%28g%29%5Crightleftharpoons%203Z%28g%29)
The relation between
and
are :
![K_p=K_c\times (RT)^{\Delta n}](https://tex.z-dn.net/?f=K_p%3DK_c%5Ctimes%20%28RT%29%5E%7B%5CDelta%20n%7D)
where,
= equilibrium constant at constant pressure = ![3.83\times 10^{-2}](https://tex.z-dn.net/?f=3.83%5Ctimes%2010%5E%7B-2%7D)
= equilibrium concentration constant = ?
R = gas constant = 0.08206 L⋅atm/(K⋅mol)
T = temperature = ![119^oC=273+119=392K](https://tex.z-dn.net/?f=119%5EoC%3D273%2B119%3D392K)
= change in the number of moles of gas = [3 - (2 + 1)] = 0
Now put all the given values in the above relation, we get:
![3.83\times 10^{-2}=K_c\times (0.08206L.atm/K.mol\times 392K)^{0}](https://tex.z-dn.net/?f=3.83%5Ctimes%2010%5E%7B-2%7D%3DK_c%5Ctimes%20%280.08206L.atm%2FK.mol%5Ctimes%20392K%29%5E%7B0%7D)
![K_c=3.83\times 10^{-2}](https://tex.z-dn.net/?f=K_c%3D3.83%5Ctimes%2010%5E%7B-2%7D)
The value of
is, ![3.83\times 10^{-2}](https://tex.z-dn.net/?f=3.83%5Ctimes%2010%5E%7B-2%7D)