A chemical system within a sealed 1 L reaction vessel is described by the following reversible reaction equation:
2H2S(g) <---> 2H(g) + S2(g)
If the equilibrium constant is 0.000 004 200 at 1103 K find:
(a) the reaction quotient intially
(b) the order of concentration of all three components at equilibrium without using calculations (From Greatest to lowest concentration)
(c) what the size of the reaction quotient indicates regarding the extent of the forward reaction
(d) the quilibrium concentration of sulphur gas if 0.070 mol of hydrogen sulphide gas is intially placed in the vessel
How I did a) was that I know that the equation for the reaction quotient was products/reactants. In this situation however, since I already have 0 moles of both products it would immediately mean that any number divided by 0 is 0.
For b) since I know that the Keq is a very small number, then that must mean that the reactants must also be a very small number. Next since it takes 2 moles of hydrogen gas for each sulfur gas, that tells me that the greatest is H2 then S2 then H2S
For c) Since I know the reaction quotient is 0 then that means that the forward reaction is very minimal or even close to not occurring.
Secondly:
For d)..... the Keq expression is [H2]^2[S2]/[H2S]^2 correct?
However, when I reach the part 4x^3/0.0049-0.28x+4x^2 I am stuck. Any help would be appreciated.
When you reach that point you have not copied the complete equation. What you have is
K = 4.2E-6 = 4X^3/(0.07-2x)^2.
When I expand the denominator I obtained
4.2E-6 = 4X^3/0.0049-0.14x + 4X^2
To proceed you "cross multiply" and get
4.2E-6 * (0.0049 - 0.14x + 4X^2) = 4X^3
Then solve for X.
By the way, I applaud your reasoning for a and b and c.
the previous answer is correct up to the second point about expanding the denominator where the second coefficient should be -0.28?
For part (a), you correctly identified that the reaction quotient (Q) is the ratio of the concentrations of the products to the concentrations of the reactants, with each concentration raised to the power of its stoichiometric coefficient in the balanced equation.
Since the reaction starts with 0 moles of both products, the concentrations of the products are initially 0. And since you have 0.070 mol of hydrogen sulfide gas initially, the concentration of H2S is 0.070 mol/L.
Therefore, the reaction quotient initially (Q) is equal to 0/(0.070)^2 = 0.
For part (b), you correctly reasoned that the order of concentration of the components at equilibrium, from greatest to lowest, is H2, S2, and H2S. This is because the equilibrium constant (K) is very small, indicating that the concentrations of the reactants are much larger than the concentrations of the products at equilibrium.
For part (c), you inferred correctly that since the reaction quotient (Q) is 0 (initially) and the equilibrium constant (K) is a very small number, the forward reaction is favoring the reactants and is not proceeding significantly in the forward direction. The size of the reaction quotient indicates that the reactants are present in excess compared to the products at equilibrium.
For part (d), you are correct that the equilibrium constant expression is K = [H2]^2[S2] / [H2S]^2.
To solve the equilibrium concentration of S2 gas, you can use the equilibrium expression and the initial concentration of H2S gas (0.070 mol/L). You can assume that x mol/L of H2 and S2 are formed at equilibrium, and thus, the concentration of H2 is 2x and the concentration of S2 is x at equilibrium.
Substituting these values into the equilibrium constant expression, you get:
K = (2x)^2 * x / (0.070 - x)^2
Simplifying this expression gives:
0.000004200 = 4x^3 / (0.070 - x)^2
To solve this equation, you can multiply both sides by (0.070 - x)^2 and rearrange the resulting cubic equation:
0.000004200 * (0.070 - x)^2 = 4x^3
Simplify further to get:
4x^3 - 0.2896x^2 + 0.0049x - 0.000000882 = 0
At this point, you can use numerical methods or approximate solutions to solve for x (the concentration of S2 at equilibrium).