Calculate the H⁺ ion concentration in lemon juice having a pH of 2.40. A)4.0 × 10^-2 M B)250 M C)0.38 M D)4.0 × 10^-3 M E)12 M

Question

Quizplus · Accepted Answer

Lemon juice is an acidic solution, therefore we can assume that the majority of the hydrogen ions are coming from H3O+.
Using the pH to find the H3O+ ion concentration: 
pH = -log[H3O+]
2.40 = -log[H3O+]
[H3O+] = 10^-pH = 10^-2.40 = 0.004 × 10^-3 M
The dissociation of the acid in the lemon juice is as follows:
HS1U1P1 --> H+ + S1U1P1-1
S1U1P1-1 --> H+ + S1S1P0
So, to find [HS1U1P1] we use the expression for Ka1:
Ka1 = [H+][S1U1P1-1]/[HS1U1P1]
4.4 × 10^-2 = (0.004 × 10^-3)([S1U1P1-1]) / [HS1U1P1]
[S1U1P1-1] / [HS1U1P1] = (Ka1 / [H+]) = (4.4 × 10^-2 / 0.004 × 10^-3) = 11
We know that [HS1U1P1] + [S1U1P1-1] = total acid concentration, which is equal to the H3O+ concentration:
[H3O+] = [HS1U1P1] + [S1U1P1-1]
0.004 × 10^-3 M = [HS1U1P1] + (11[HS1U1P1])
[HS1U1P1] = 0.004 × 10^-3 / 12 = 0.333 × 10^-3 M 
Finally, to find the total concentration of the two ions:
[HS1U1P1] + [S1S1P0] = 0.333 × 10^-3 M + 0.004 × 10^-3 M = 0.00433 × 10^-3 M = 4.33 × 10^-6 M = 4.0 × 10^-3 M,
which is equivalent to 4.0 × 10^-3 M, giving us choice D as the correct answer.

Calculate the H+ Ion Concentration in Lemon Juice Having a PH

Calculate the H⁺ Ion Concentration in Lemon Juice Having a PH