Answer : The equilibrium concentration of [tex]PCl_3[/tex] is, 1.0 M
Explanation : Given,
Equilibrium concentration of [tex]PCl_5[/tex] = 0.26 M
Volume of solution = 1.00 L
Equilibrium constant [tex](K_c)[/tex] = 4.0
The balanced equilibrium reaction will be,
[tex]PCl_5\rightleftharpoons PCl_3+Cl_2[/tex]
The expression of equilibrium constant for the reaction will be:
[tex]K_c=\frac{[PCl_3][Cl_2]}{[PCl_5]}[/tex]
From the reaction we conclude that the concentration of [tex]PCl_3[/tex] and [tex]Cl_2[/tex] are equal.
Let the concentration of [tex]PCl_3[/tex] be 'X'.
So, concentration of [tex]Cl_2[/tex] = X
Now put all the values in this expression, we get :
[tex]4.0=\frac{(X)\times (X)}{0.26}[/tex]
[tex]4.0=\frac{(X)^2}{0.26}[/tex]
[tex]X=1.0M[/tex]
Thus,
The concentration of [tex]PCl_3[/tex] at equilibrium = X = 1.0 M
The concentration of [tex]Cl_2[/tex] at equilibrium = X = 1.0 M