the equilibrium constant for the synthesis of HBr(g0 from hydrogen and bromine gas is 2.18*10 exponent 6 at 730 degrees celcius.if 3.75 mol of HBr(g) is put into a 15L reaction vessel,calculate the concentration of H2,Br2 and HBr at equilibrium
To answer this question, we'll start by writing the balanced chemical equation for the synthesis of HBr:
H2 + Br2 ⇌ 2HBr
According to the equilibrium constant expression, Kc, the concentration of products (HBr) is raised to the power of their stoichiometric coefficient (2), and the concentration of reactants (H2 and Br2) is multiplied. Therefore, we can write the equilibrium constant expression as follows:
Kc = [HBr]^2 / ([H2] * [Br2])
Given that the equilibrium constant, Kc, is 2.18 × 10^6 and the initial concentration of HBr is 3.75 mol in a 15 L reaction vessel, we can set up the equilibrium concentration table.
Let's assume the equilibrium concentration of H2 is x mol/L, the equilibrium concentration of Br2 is y mol/L, and the equilibrium concentration of HBr is z mol/L.
Using the given initial concentrations and the stoichiometry of the balanced equation, we can set up the following table:
H2 + Br2 ⇌ 2HBr
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Initial: ? ? 3.75 mol / 15 L
Change: -x -y +2z
Equilibrium: x y 3.75/15 + 2z
At equilibrium, we can substitute the equilibrium concentrations into the equilibrium constant expression:
2.18 × 10^6 = (3.75/15 + 2z)^2 / (x * y)
Since the volume is given as 15L, we can cancel it out from the equation. Simplifying further, we get:
2.18 × 10^6 = (0.25 + 2z)^2 / (x * y)
Now, we need more information to determine the concentrations of x, y, and z. One possible approach is to assume that x and y are negligible compared to 0.25. This assumption is valid if the equilibrium constant is large, indicating that the forward reaction is favored.
If we assume x = y = 0, we can simplify the equation:
2.18 × 10^6 = (0.25 + 2z)^2 / 0
This equation tells us that 2.18 × 10^6 = ∞, which is not possible. Therefore, our assumption is incorrect, and x and y cannot be zero.
To fully solve this problem, we need additional information such as the initial concentrations of H2 and Br2.