To analyze the equilibrium concentrations for the reaction
A2(g)⇌B2(g), where the equilibrium constant
Kc at temperature
T(K) is 99.0, follow these steps:
Given:
Kc=99.0Initial moles of
A2:2 moles
Volume of the flask: 1 L
Calculation:
Initial Conditions and Definition:
Since the reaction starts with 2 moles of
A2(s) which sublimes to
A2(g), the initial concentration of
A2 is
2mol∕L (as the flask is 1 L in volume).
Setting up the Equilibrium Expression:
For the equilibrium constant expression:
Kc=‌Let the concentration of
B2 at equilibrium be
xmol∕L. Therefore, the concentration of
A2 becomes
(2−x)mol∕L at equilibrium.
Solving the Equilibrium Equation:
Substitute the equilibrium values into the
Kc expression:
99=‌Solving for
x :
‌99(2−x)=x‌198−99x=x‌198=100x‌x=1.98Thus, the concentration of
B2 is
[B2]=1.98mol∕L.
Finding the Concentration of
A2 :
Calculate
[A2] using the expression
2−x :
[A2]=2−1.98=0.02mol∕LConclusion:
The concentrations at equilibrium are:
‌[A2]=0.02mol∕L‌[B2]=1.98mol∕L