Hydrogen iodide decomposes according to the following equation:
H2(g) + I2(g) ⇌ 2HI(g)
A 2.50 L equilibrium mixture contains 0.0875 mol H2, 0.020 mol I2, and 3.72 mol HI. Determine the new equilibrium concentrations after 1.25 mol HI are added to the system.
This is what I've done so far, I made this ICE table:
IE (M): 0.0350 0.0800 1.488
D(M): +0.500
NI(M): 0.0350 0.0800 1.988
C(M): -x -x +2x
NE(M): 0.0350-x 0.0800-x 1.988+2x
Is this correct? what do I do next?
First, that 0.020/2.5L = 0.008 and not 0.08.
Second, you wrote the equation as a synthesis and not a decomposition. That doesn't make that much difference as long as you keep Keq straight.
Third, if you add 0.5 M HI to the system which is already at equilibrium, the system will shift away from HI and to H2 and I2; therefore, those should be +x and +x and HI is not -2x/
Fourth, you should calculate Keq for the system as you view it; i.e., as a decomposition or as a synthesis.
Post your work if you get stuck.
Your ICE table looks correct so far. The next step is to determine the expression for the equilibrium constant (K) and set up the equation based on the balanced equation.
The equilibrium expression for the given reaction is:
K = (HI)^2 / (H2)(I2)
Substituting the values from the ICE table:
K = (1.988+2x)^2 / (0.0350-x)(0.0800-x)
Now, you need to set up an equation using the given information that 1.25 mol of HI is added to the system. Since HI is a product, its concentration in the NE (new equilibrium) row will increase by 1.25 mol. So you can substitute (1.988+2x + 1.25) for (1.988+2x) in the equilibrium expression.
K = [(1.988+2x + 1.25)^2 / (0.0350-x)(0.0800-x)]
Now, you can solve for x by setting up an equation where K and the given concentrations are known. In this case, the concentrations are:
[H2] = 0.0875 mol / 2.50 L = 0.0350 M
[I2] = 0.020 mol / 2.50 L = 0.0800 M
[HI] = 3.72 mol / 2.50 L = 1.488 M
Substituting these values into the equilibrium expression, you can solve for x:
K = [(1.988+2x + 1.25)^2 / (0.0350-x)(0.0800-x)]
Simplifying the expression and plugging in the given values:
K = [(3.238+2x)^2 / (0.0350-x)(0.0800-x)]
Now you have an equation that relates x and K, where K is known to be a constant. Solve this equation to find the value of x, and then substitute it back into the expressions for H2, I2, and HI to get the new equilibrium concentrations.