For the ionization of phenylacetic acid,
Hc8H7O2 +H20 <--> C8H7O2- (aq) + H3o+ (aq) Ka + 4.9x10^-5
What is the concentration of the phenylacetic ion, C8H702,- in 0.186 M phenylacetic acid, HC8H702?
Call it HP.
...............HP ==> H^+ + P^-
initial....0.186M......0....0
change........-x.......x.....x
equil.....0.186-x......x......x
Ka = (H^+)(P^-)?(HP)
Substitute from the ICE chart, solve for x = H^+ = P^-
To find the concentration of the phenylacetic ion (C8H7O2-) in a solution of phenylacetic acid (HC8H7O2), you can use the equation for the equilibrium constant (Ka) and the given information about the concentration of phenylacetic acid.
The equation for the ionization of phenylacetic acid is:
HC8H7O2 + H2O ⇌ C8H7O2- + H3O+
The equilibrium constant Ka is given as 4.9x10^-5.
Let's assume that at equilibrium, x moles of phenylacetic acid ionize to form x moles of phenylacetic ion (C8H7O2-) and x moles of H3O+.
Since the initial concentration of phenylacetic acid (HC8H7O2) is 0.186 M, the concentration of phenylacetic ion (C8H7O2-) at equilibrium can be represented as (0.186 - x) M.
Using the equation for Ka, we can write the expression for the equilibrium constant:
Ka = [C8H7O2-][H3O+] / [HC8H7O2]
Substituting the values we know:
4.9x10^-5 = (0.186 - x)(x) / 0.186
Now we can solve this equation to find the value of x, which will give us the concentration of phenylacetic ion (C8H7O2-).
1. Multiply both sides of the equation by 0.186 to eliminate the denominator:
4.9x10^-5 * 0.186 = (0.186 - x)(x)
2. Simplify:
9.114x10^-6 = 0.186x - x^2
3. Rearrange and convert to quadratic form:
x^2 - 0.186x + 9.114x10^-6 = 0
4. Solve the quadratic equation using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -0.186, and c = 9.114x10^-6.
Using the quadratic formula, calculate the two possible values of x. Since it represents a concentration, it must be positive. Choose the positive value for further calculations.
5. Once you have obtained the value of x, substitute it back into the expression (0.186 - x) to find the concentration of the phenylacetic ion (C8H7O2-).
Therefore, by solving the equation using the given Ka value and concentration of phenylacetic acid, you will be able to determine the concentration of the phenylacetic ion in the solution.