Consider an equation x ->2y (in equilibrium) with equilibrium constant...
Equation and Equilibrium Constant
The given equation is x -> 2y and its equilibrium constant is kc=3.6M at 298k.
Initial Concentrations
The initial concentrations are [x]=1.0M and [y]=0M.
Equilibrium Concentration of X
To determine the equilibrium concentration of x, we need to use the equilibrium constant expression:
kc = [y]^2 / [x]
We can rearrange this equation to solve for [x]:
[x] = [y]^2 / kc
Since the initial concentration of y is 0M, we need to use the stoichiometry of the reaction to find the amount of y that will be produced at equilibrium. For every 1 mole of x that is consumed, 2 moles of y will be produced. Therefore, at equilibrium, the concentration of y will be:
[y] = 2[x]
Substituting this expression for [y] into the equation for [x], we get:
[x] = (2[x])^2 / kc
Simplifying this expression, we get:
[x] = 4[x]^2 / kc
Multiplying both sides by kc and rearranging, we get a quadratic equation:
4[x]^2 - kc[x] = 0
Solving for [x] using the quadratic formula, we get:
[x] = kc / (2*2) = 0.40M
Therefore, the equilibrium concentration of x at 298k is 0.40M, which is option (c).
Consider an equation x ->2y (in equilibrium) with equilibrium constant...