Question

In the reaction:
$A\left(g\right)+3B\left(g\right)\rightleftharpoons 4C\left(g\right)$
the initial concentration of $A$ is equal to that of $B$. The equilibrium concentration of $A$ and $C$ are equal.
What is the value of its equilibrium constant $K_c$

Answer 1

In the reaction:
$A\left(g\right)+3B\left(g\right)\rightleftharpoons 4C\left(g\right)$
the initial concentration of $A$ is equal to that of $B$. The equilibrium concentration of $A$ and $C$ are equal.
The value of its equilibrium constant $K_c$ is $8$.
Let the initial concentration of A $=$ the initial concentration of B $=$ x M.
Let y M of reacts with 3 y M of B to form 4 y M of C at equilibrium.
$x-y$ M of A and $x-3y$ M of B remain at equilibrium.
The equilibrium concentration of $A$ and $C$ are equal.
$x-y=4y$
$x=5y$
$y=0.2x$
$x-y=x-0.2x=0.8x$ M of A, $x-3y=x-3\left(0.2x\right)=0.4x$ M of B and $4y=4\left(0.2x\right)=0.8x$ M of C remain at equilibrium.
$K_c=\frac{[C{]}^4}{\left[A\right][B{]}^3}$
$K_c=\frac{(0.8x{)}^4}{\left(0.8x\right)\times (0.4x{)}^3}$
$K_c=\frac{(0.8x{)}^4}{\left(0.8x\right)\times (0.4x{)}^3}$
$K_c=8$