Lactic acid, HC3H5O3(aq) is a weak acid that gives yougurt its sour taste(Yeeeeecccckkk). Calculate the pH of a 0.0010 mol/L solution of Lactic acid. The Ka for lactic acid is 1.4 x 10^-4
Let's call Lactic acid HL.
HL ==> H^+ + L^-
Ka = (H^+)(L^-)/(HL) = 1.4 x 10^-4
initially before ionization:
(HL) = 0.001 M
(H^+) = 0
(L^-) = 0
change:
(H^+) = +x
)L^-) = +x
(HL) = 0.001 - x
equilibrium:
(H^+) = +x
(L^-) = +x
(HL) = 0.001 - x
Substitute the equilibrium values shown into the Ka expression and solve for x.
Then convert (H^+) to pH by pH = -log(H^+)
2.5
To find the pH of the lactic acid solution, we need to calculate the concentration of H+ ions in the solution first using the acid dissociation constant (Ka) for lactic acid.
The equation for the dissociation of lactic acid (HC3H5O3) can be written as:
HC3H5O3 ⇌ H+ + C3H5O3-
The Ka expression for this equilibrium is:
Ka = [H+][C3H5O3-] / [HC3H5O3]
Given that the initial concentration of lactic acid is 0.0010 mol/L, the initial concentration of H+ and C3H5O3- is equal.
Let's assume the concentration of H+ ions formed is x. Then, the concentrations of C3H5O3- and HC3H5O3 would also be x, as one mole of lactic acid dissociates to produce one mole of H+ ions and one mole of C3H5O3- ions.
Therefore, the equation for Ka can be rewritten as:
Ka = x * x / (0.0010 - x)
Given that Ka is 1.4 x 10^-4, we can substitute these values into the equation:
1.4 x 10^-4 = x^2 / (0.0010 - x)
Now, we can simplify this equation:
1.4 x 10^-4 * (0.0010 - x) = x^2
0.0014 - 1.4 x 10^-4x = x^2
Bringing all terms to one side yields:
x^2 + 1.4 x 10^-4x - 0.0014 = 0
This is a quadratic equation. We can solve it using the quadratic formula:
x = [-b ± √(b^2 - 4ac)] / (2a)
In this case, a = 1, b = 1.4 x 10^-4, and c = -0.0014. Substituting these values:
x = [-1.4 x 10^-4 ± √((1.4 x 10^-4)^2 - 4(1)(-0.0014))] / (2(1))
Calculating the square root inside the square root and simplifying, we get:
x ≈ 0.011 M or x ≈ -0.011 M
Since the concentration of H+ ions cannot be negative, we discard the negative value. Therefore, the concentration of H+ ions in the lactic acid solution is approximately 0.011 M.
To calculate the pH of the solution, we can use the equation:
pH = -log[H+]
pH = -log(0.011)
Using a calculator, we find:
pH ≈ 1.96
Therefore, the pH of a 0.0010 mol/L solution of lactic acid is approximately 1.96.
To calculate the pH of a solution of lactic acid, we need to consider the ionization of lactic acid and the equilibrium expression for its acid dissociation.
The balanced equation for the ionization of lactic acid is:
HC3H5O3 ⇌ H+ + C3H5O3-
The equilibrium constant expression for this reaction is given by the acid dissociation constant (Ka):
Ka = [H+][C3H5O3-]/[HC3H5O3]
The concentration of H+ in the solution is the same as the concentration of the dissociated lactic acid, which is equal to x.
Thus, the equilibrium constant expression becomes:
Ka = x^2/(0.0010 - x)
Since the Ka value for lactic acid is given as 1.4 x 10^-4, we can substitute these values into the equation:
1.4 x 10^-4 = x^2/(0.0010 - x)
Now, we can solve this equation to find the value of x, which represents the concentration of H+ ions. Rearranging the equation gives:
x^2 = 1.4 x 10^-4 * (0.0010 - x)
Expanding this expression further, we get:
x^2 = 1.4 x 10^-4 * 0.0010 - 1.4 x 10^-4 * x
x^2 + 1.4 x 10^-4 * x - 1.4 x 10^-7 = 0
We can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
In this case, a = 1, b = 1.4 x 10^-4, and c = -1.4 x 10^-7. Substituting these values into the quadratic formula, we can find the values for x.