What is the hydroxide-ion concentration of a 0.240 M oxalic acid, H2C2O4, solution? For
oxalic acid, Ka1 = 5.6 × 10–2 and Ka2 = 5.1 × 10–5.
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To find the hydroxide-ion concentration of the oxalic acid solution, we need to first calculate the concentration of the hydroxide ions (OH-) produced when the oxalic acid dissociates.
Oxalic acid, H2C2O4, has two dissociation steps. The first step involves the loss of one hydrogen ion, and the second step involves the loss of another hydrogen ion.
The balanced dissociation equation for the first dissociation step is:
H2C2O4 ⇌ HC2O4- + H+
The balanced dissociation equation for the second dissociation step is:
HC2O4- ⇌ C2O4^2- + H+
From the given Ka values, we can determine the equilibrium constant (Kb) for the hydroxide-ion concentration in each step. The equilibrium constant for the first dissociation is equal to the reciprocal of the Ka1 value, and the equilibrium constant for the second dissociation is equal to the reciprocal of the Ka2 value.
Kb1 = 1/Ka1 = 1/(5.6 × 10^-2)
Kb2 = 1/Ka2 = 1/(5.1 × 10^-5)
Next, we can set up the concentration table and equilibrium expressions for each dissociation step.
For the first dissociation step:
[H2C2O4] ----- [HC2O4-] + [H+]
Initial: --------- 0.240 M --- 0 M
Change: --------- -x -------- +x
Equilibrium: -- 0.240-x --- x
For the second dissociation step:
[HC2O4-] ----- [C2O4^2-] + [H+]
Initial: --------- x -------- 0 M
Change: -------- -x -------- +x
Equilibrium: -- x ------------ x
Since the concentration of hydroxide ions (OH-) is equal to the concentration of the second dissociation step, the concentration of OH- in the solution is also x.
To find x, we need to set up the equilibrium expressions for each dissociation step and solve for x.
The equilibrium expression for the first dissociation step is:
Kb1 = [HC2O4-][H+]/[H2C2O4] = x(0.240-x)/(0.240)
The equilibrium expression for the second dissociation step is:
Kb2 = [C2O4^2-][H+]/[HC2O4-] = x/x = 1
Now, we can solve the equation Kb1 = x(0.240-x)/(0.240) for x. Substitute the given values and solve for x using algebraic methods.
Kb1 = (5.6 × 10^-2) = x(0.240-x)/(0.240)
Solve this equation to find the value of x, which represents the concentration of hydroxide ions (OH-) in the solution.