Calculate the pH of a solution that contains 2.4 × 10^-⁸ M H₃O⁺ at 25°C. A) 2.40 B) 6.38 C) 7.62 D) 5.38 E) 8.62

Question

Quizplus · Accepted Answer

Step 1: Write the balanced equation for the dissociation of HS1U1B13S1U1B0O⁺:

HS1U1B13S1U1B0O⁺ ⇌ H⁺+ S1U1B13S1U1B0O (Ka = 1.1 × 10S1U1P1-S1S1P0S1U1P9S1S1P0)

Step 2: Write the expression for Ka and the equilibrium concentration of HS1U1B13S1U1B0O⁺:

Ka = [H⁺][S1U1B13S1U1B0O]/[HS1U1B13S1U1B0O⁺]
[HS1U1B13S1U1B0O⁺] = 2.4 × 10S1U1P1-S1S1P0S1U1P18S1S1P0 M

Step 3: Calculate the concentration of H⁺:

Ka = [H⁺][S1U1B13S1U1B0O]/[HS1U1B13S1U1B0O⁺]
10-S1U1P1-S1S1P0S1U1P9S1S1P0 = [H⁺](2.4 × 10S1U1P1-S1S1P0S1U1P18S1S1P0)/(2.4 × 10S1U1P1-S1S1P0S1U1P18S1S1P0 - [H⁺])
Simplifying the equation gives:
[H⁺]² + 1.1 × 10S1U1P1-S1S1P0S1U1P9S1S1P0[H⁺] - (1.1 × 10S1U1P1-S1S1P0S1U1P9S1S1P0)(10-S1U1P1-S1S1P0S1U1P9S1S1P0) = 0
Using the quadratic formula, we get:
[H⁺] = 7.62 × 10-S1U1P1

Step 4: Calculate the pH:

pH = -log[H⁺]
pH = -log(7.62 × 10-S1U1P1)
pH = 7.62

Calculate the PH of a Solution That Contains 2