Calcium lactate is a salt of weak organic acid and strong base, represented as Ca(Lac)2. A saturated solution of Ca(Lac)2 contains 0.13 mole of this salt in 0.50 L solution. The pOH of this solution is 5.60. Assuming a complete dissociation of the salt, calculate Ka of lactic acid.[In the multiple of 10–4, up to first decimal place]Correct answer is between '8.2,8.4'. Can you explain this answer?

Question

Calcium lactate is a salt of weak organic acid and strong base, represented as Ca(Lac)2. A saturated solution of Ca(Lac)2 contains 0.13 mole of this salt in 0.50 L solution. The pOH of this solution is 5.60. Assuming a complete dissociation of the salt, calculate Ka of lactic acid.[In the multiple of 10&ndash;4, up to first decimal place]Correct answer is between '8.2,8.4'. Can you explain this answer?

Answer

For hydrolysis of weak acid and strong base ,PH=1/2(pkw+pka+loga) here a is lactate ion conc =2*.26 ,ph =14-poh
14-5.6= 1/2(14-logka+log.52)
logka =-3.084 thus
ka=8.24 ,*10-4

Answer

To find the Ka of lactic acid, we first need to find the concentration of lactic acid in the solution.

Since calcium lactate (Ca(Lac)2) completely dissociates in solution, we can assume that 0.13 moles of calcium lactate dissociate to form 0.26 moles of lactic acid.

The volume of the solution is 0.50 L, so the concentration of lactic acid is 0.26 moles / 0.50 L = 0.52 M.

Now, we need to find the concentration of hydroxide ions (OH-) in the solution. The pOH is given as 5.60, so the concentration of hydroxide ions can be calculated using the equation:

pOH = -log[OH-]

5.60 = -log[OH-]

[OH-] = 10^(-5.60) = 2.51 x 10^(-6) M

Since the concentration of hydroxide ions is equal to the concentration of lactic acid (assuming a 1:1 stoichiometry), the concentration of lactic acid is also 2.51 x 10^(-6) M.

Now, we can use the equilibrium equation for lactic acid to find the Ka:

Ka = [H+][Lac-] / [HLac]

Since the concentration of lactic acid is equal to the concentration of hydroxide ions, we can substitute 2.51 x 10^(-6) M for both [H+] and [Lac-]:

Ka = (2.51 x 10^(-6) M)(2.51 x 10^(-6) M) / (0.52 M)

Ka = 6.3 x 10^(-12)

Therefore, the Ka of lactic acid is 6.3 x 10^(-12) (in the multiple of 10).

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