A l.00L flask contains 4.40mol of HI at a certain temperature. The Keq at this temperature is 5.0 * 10^-4. What are the concentrations of H2 and I2 at equilibrium?

To find the concentrations of H2 and I2 at equilibrium, we need to use the equilibrium expression and the initial concentration of HI. The equilibrium expression for the reaction is:

Keq = [H2][I2] / [HI]

Given that Keq = 5.0 * 10^-4 and the initial concentration of HI is 4.40 mol, we can work backward to find the concentrations of H2 and I2 at equilibrium.

First, let's assume that the concentrations of H2 and I2 at equilibrium are x (in mol/L). Since the initial concentration of HI is 4.40 mol, the equilibrium concentration of HI is (4.40 - x) mol/L.

Now, substitute these values into the equilibrium expression:

5.0 * 10^-4 = x * x / (4.40 - x)

We can solve this equation to find the value of x, which represents the concentrations of H2 and I2 at equilibrium.

To solve the equation, we need to rearrange it and then solve the resulting quadratic equation:

5.0 * 10^-4 = x^2 / (4.40 - x)

Rearrange:

5.0 * 10^-4 * (4.40 - x) = x^2

Multiply both sides:

2.2 * 10^-3 - 5.0 * 10^-4 * x = x^2

Rewrite in standard form:

x^2 + 5.0 * 10^-4 * x - 2.2 * 10^-3 = 0

Use the quadratic formula to solve for x:

x = (-b ± √(b^2 - 4ac))/(2a)

In our case, a = 1, b = 5.0 * 10^-4, c = -2.2 * 10^-3. Plugging in the values:

x = (-5.0 * 10^-4 ± √((5.0 * 10^-4)^2 - 4 * 1 * -2.2 * 10^-3))/(2 * 1)

Solving this equation will give us the two possible values for x, representing the concentrations of H2 and I2 at equilibrium.