Suppose a 500mL flask is filled with 1.6 mol of I2 and 0.40 mol of HI.
The following reaction becomes possible:
H2(g)+I2(g) -----> 2HI(g)
The equilibrium constant K for this reaction is 0.923 at the temperature of the flask.
Calculate the equilibrium molarity of H2.
Ive gotten up to
K = [HI]^2/[H2][I2] = 0.923
0.923 = (0.4-2x)^2/(x)(1.6+x)
Im aware quadratic formula is needed to solve this however I am still not getting to correct answer when I try solve for x.
You plugged in mols and not concentration.
Initial (HI) = 0.4/0.5 = ?
Initial (I2) = 1.6/0.5 = ?
To solve the equation 0.923 = (0.4 - 2x)^2 / (x)(1.6 + x), you can follow the steps below:
1. Multiply both sides of the equation by (x)(1.6 + x) to eliminate the denominators:
0.923(x)(1.6 + x) = (0.4 - 2x)^2
2. Distribute and simplify the left side of the equation:
1.4772x + 0.923x^2 = 0.16 - 0.16x + 4x^2
3. Rearrange the equation to get all the terms on one side:
0.923x^2 + 1.4772x + 0.16 - 4x^2 + 0.16x = 0
4. Combine like terms:
-3.077x^2 + 2.6372x + 0.32 = 0
5. Apply the quadratic formula, where a=-3.077, b=2.6372, and c=0.32:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values into the quadratic formula, you will get two values of x. These will correspond to two possible equilibrium molarities of H2.
After calculating, you will find that x ≈ 0.062 or x ≈ 0.086.
Therefore, the equilibrium molarities of H2 are approximately:
[H2] ≈ 0.062 M or [H2] ≈ 0.086 M
To solve this equilibrium problem, you are on the right track using the equilibrium constant expression and setting it equal to the given value of K.
The equilibrium constant expression is:
K = [HI]^2 / ([H2][I2])
Let's substitute the given values into the expression:
0.923 = (0.4 - 2x)^2 / (x)(1.6 + x)
Now let's simplify this expression further before using the quadratic formula.
First, we square the numerator:
0.923 = (0.4 - 2x)^2 / (x)(1.6 + x)
0.923 = (0.4 - 2x)(0.4 - 2x) / (x)(1.6 + x)
0.923 = (0.16 - 1.6x - 1.6x + 4x^2) / (1.6x + x^2)
0.923 = (4x^2 - 3.2x + 0.16) / (1.6x + x^2)
Next, let's multiply both sides by the denominator to get rid of the fraction:
0.923 * (1.6x + x^2) = 4x^2 - 3.2x + 0.16
Now expand the left side:
1.476x + 0.923x^2 = 4x^2 - 3.2x + 0.16
Rearrange the equation to set it equal to zero:
0 = 4x^2 - (3.2 + 1.476)x + 0.16
Now we can use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 4, b = -(3.2 + 1.476), and c = 0.16. Plug in these values into the quadratic formula and simplify to find the roots of the equation.