2 NOCl(g) --> 2 NO(g) + Cl2(g)
Let’s assume that at a given temperature the equilibrium constant is 2.25: Also, the equilibrium concentration of the NOCl is 0.04M. Determine the concentration of the NO and the Cl2
CLUE: the concentration of both of the products must be equal if we started only from NOCl, since they are in a 1:1 ration. Since you don’t know the concentration of either of the products, use the variable ‘x’ to represent their concentration.
First, I don't buy that NO and Cl2 are equal and for exactly the reason the hint points out. The products are NOT a 1:1 ratio. (NO) must be twice the (Cl2).
.........2NOCl(g) --> 2NO(g) + Cl2(g)
equilib....0.04M.........2x.......x
K = 2.25 = (NO)^2(Cl2)/(NOCl)^2
2.25 = (2x)^2(x)/(0.04)^2
Solve for x = (Cl2), then 2x = (NO).
To determine the concentration of NO and Cl2 in the given equilibrium reaction, we can set up an ICE (Initial, Change, Equilibrium) table and solve for the unknowns.
1. Write the balanced chemical equation:
2 NOCl(g) ⟶ 2 NO(g) + Cl2(g)
2. Set up the ICE table:
| NOCl(g) | NO(g) | Cl2(g) |
------------------------------------------------------------------
Initial | 0.04M | 0M | 0M |
Change | -2x | +2x | +x |
Equilibrium | 0.04 - 2x | 2x | x |
Here, 'x' represents the change in concentration from the initial state to equilibrium for both NO(g) and Cl2(g). We subtract 2x from the initial concentration of NOCl(g) because each NOCl(g) molecule contributes -2x to the reaction (according to the stoichiometry of the balanced equation).
3. Set up the equilibrium expression using the given equilibrium constant (K):
K = [NO(g)]^2 [Cl2(g)] / [NOCl(g)]^2
Given that K = 2.25, we can substitute the equilibrium concentrations into the equilibrium expression:
2.25 = (2x)^2 * x / (0.04 - 2x)^2
4. Solve for 'x':
2.25 = 4x^3 / (0.04 - 2x)^2
Expanding the expression, we get:
2.25 = 4x^3 / (0.0016 - 0.16x + 4x^2)
Cross-multiplying, we obtain:
2.25 * (0.0016 - 0.16x + 4x^2) = 4x^3
Multiplying and rearranging, we have:
0.0036 - 0.36x + 0.09x^2 - 4x^3 = 0
This is a cubic equation that we can solve using numerical methods or a graphing calculator to find the value of 'x'. The value of 'x' will represent the equilibrium concentration of both NO(g) and Cl2(g) in moles per liter (M).
Once you find the value of 'x', you can substitute it back into the ICE table equations to calculate the concentrations of NO(g) and Cl2(g) at equilibrium.