To determine the pH that leads to the greatest concentration of hydrogen oxalate, we need to consider the acid dissociation constant (Ka) of oxalic acid (H2C2O4), which will help us determine the concentration of hydrogen oxalate (HC2O4-) at different pH levels.
The Ka expression for the dissociation of oxalic acid is as follows:
H2C2O4 ⇌ H+ + HC2O4-
The dissociation constant expression is given by:
Ka = [H+][HC2O4-] / [H2C2O4]
At equilibrium, the concentrations of H+ and HC2O4- are equal, so we can simplify the expression to:
Ka = [H+]^2 / [H2C2O4]
Taking the square root of both sides:
[H+] = sqrt(Ka * [H2C2O4])
Now, we can analyze the given pH values and calculate the concentration of hydrogen oxalate at each pH level using the equation above.
pH 1.23: [H+] = 10^(-pH) = 10^(-1.23) = 0.0562
pH 2.71: [H+] = 10^(-pH) = 10^(-2.71) = 0.000207
pH 4.19: [H+] = 10^(-pH) = 10^(-4.19) = 5.283 x 10^(-5)
pH 7.65: [H+] = 10^(-pH) = 10^(-7.65) = 2.480 x 10^(-8)
Now, using the calculated [H+] values, we can determine the concentration of hydrogen oxalate (HC2O4-) at each pH level. Since the initial concentration of oxalic acid (H2C2O4) is assumed to be the same in each case, we can directly compare the [HC2O4-] values.
Therefore, based on the calculations above, the pH that leads to the greatest concentration of hydrogen oxalate is pH 1.23.