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?
Please explain the steps as well..thank you so much
Ka=x^2/(.186-x)
x^2=4.9E-5(.186-x)
1/4.9E-5 x^2 +x -.186=0
use the quadratic equation.
To find the concentration of the phenylacetic ion (C8H7O2-) in a 0.186 M phenylacetic acid (HC8H7O2), you can use the given equilibrium constant (Ka) and the expression for the ionization reaction.
Step 1: Write down the ionization reaction:
HC8H7O2 + H2O ⇌ C8H7O2- + H3O+
Step 2: Write down the equilibrium expression using the given Ka value:
Ka = [C8H7O2-][H3O+] / [HC8H7O2]
Step 3: Identify the initial concentration of phenylacetic acid (HC8H7O2) and the change in concentration of the phenylacetic ion (C8H7O2-).
The initial concentration of phenylacetic acid, [HC8H7O2]initial, is given as 0.186 M.
The change in concentration of the phenylacetic ion, [C8H7O2-], is not known and will be denoted as "x".
The concentration of the hydronium ion, [H3O+], will also be "x" initially, as it is produced in a 1:1 ratio with the phenylacetic ion.
Step 4: Write the values into the equilibrium expression:
Ka = [C8H7O2-][H3O+] / [HC8H7O2]
Ka = (x)(x) / (0.186)
Step 5: Solve for "x" using the given Ka value:
Ka = 4.9x10^-5
4.9x10^-5 = (x)(x) / (0.186)
4.9x10^-5 = x^2 / 0.186
Multiplying both sides of the equation by 0.186:
4.9x10^-5 * 0.186 = x^2
9.114x10^-6 = x^2
To simplify the calculation, take the square root of both sides:
x = √(9.114x10^-6)
x ≈ 9.55x10^-3
Step 6: Calculate the concentration of the phenylacetic ion (C8H7O2-):
The concentration of the phenylacetic ion is equal to "x", which is approximately 9.55x10^-3 M.
To find the concentration of the phenylacetic ion, C8H7O2-, in a given solution of phenylacetic acid, HC8H7O2, we can use the equilibrium expression and solve for the concentration of the ion.
Step 1: Write the balanced chemical equation for the ionization of phenylacetic acid:
HC8H7O2 + H2O ↔ C8H7O2- + H3O+
Step 2: Write the equilibrium expression using the given equilibrium constant (Ka):
Ka = [C8H7O2-][H3O+] / [HC8H7O2]
Step 3: Identify the initial concentration of phenylacetic acid:
Given: [HC8H7O2] = 0.186 M
Step 4: Assume that at equilibrium, the concentration of phenylacetic acid, [HC8H7O2], will decrease by an amount x, and the concentrations of C8H7O2- and H3O+ will increase by x.
Step 5: Substitute the initial concentration of phenylacetic acid and the changes in concentration into the equilibrium expression:
Ka = (x)(x) / (0.186 - x)
Step 6: Since the value of Ka is very small (4.9x10^-5), we can assume that the change in concentration of phenylacetic acid, x, is much smaller than the initial concentration (0.186 M). Thus, we can neglect it when subtracting it from 0.186 M.
Step 7: Simplify the equation:
Ka = x^2 / 0.186
Step 8: Rearrange the equation to solve for x:
x^2 = Ka * 0.186
Step 9: Calculate x by taking the square root of both sides of the equation:
x = √(Ka * 0.186)
Step 10: Substitute the value of Ka (4.9x10^-5) into the equation to calculate x:
x = √(4.9x10^-5 * 0.186)
Step 11: Calculate the concentration of the phenylacetic ion, [C8H7O2-]:
[C8H7O2-] = x = √(4.9x10^-5 * 0.186)
Step 12: Solve for [C8H7O2-] using a calculator or spreadsheet:
[C8H7O2-] ≈ 1.45x10^-3 M
Therefore, the concentration of the phenylacetic ion, C8H7O2-, in a 0.186 M solution of phenylacetic acid is approximately 1.45x10^-3 M.