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Calculate the pH of a solution formed by mixing 200.0 mL of 0.30 M HClO with 100.0 mL of 0.20 M KClO. The Ka for HClO is 2.9 × 10^-8.

A) 5.99
B) 8.01
C) 7.54
D) 7.06
E) 6.46

1 Answer

3 votes

Answer:

The correct answer is D) 7.06.

Step-by-step explanation:

The first step in solving this problem is to write the balanced chemical equation for the reaction that occurs when HClO and KClO are mixed:

HClO + KClO → K+ + ClO- + HClO

The reaction is a neutralization reaction in which HClO acts as an acid and KClO acts as a base.

Next, we need to calculate the moles of acid (HClO) and base (KClO) that are present in the solution after mixing. We can use the formula:

moles = concentration × volume

For HClO, we have:

moles of HClO = (0.30 mol/L) × (0.200 L) = 0.060 mol

For KClO, we have:

moles of KClO = (0.20 mol/L) × (0.100 L) = 0.020 mol

The HClO will react with the KClO to form ClO- and H3O+ ions:

HClO + ClO- → H2O + ClO2-

So, we can set up an ICE (initial, change, equilibrium) table to determine the concentration of H3O+ ions at equilibrium:

HClO ClO- H3O+

Initial 0.060 M 0.020 M 0 M

Change -x -x +x

Equilibrium 0.060-x 0.020-x x

The value of x represents the concentration of H3O+ ions at equilibrium. We can use the equilibrium concentrations to set up an expression for the acid dissociation constant (Ka) of HClO:

Ka = [H3O+][ClO-] / [HClO]

Substituting in the equilibrium concentrations, we get:

Ka = x^2 / (0.060 - x)

The value of x can be calculated using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -Ka, and c = Ka × 0.060.

After substituting these values into the quadratic formula, we get:

x = 7.63 × 10^-5 M

The pH of the solution is given by:

pH = -log[H3O+]

Substituting the value of [H3O+] into this equation, we get:

pH = -log(7.63 × 10^-5) ≈ 4.12

However, we need to consider the dilution factor when mixing the two solutions. The total volume of the solution after mixing is:

V = 200.0 mL + 100.0 mL = 300.0 mL = 0.300 L

The concentration of H3O+ ions in the final solution is:

[H3O+] = x / V = 7.63 × 10^-5 M / 0.300 L ≈ 0.00025 M

Taking the negative logarithm of this concentration gives:

pH = -log(0.00025) ≈ 3.60

Therefore, the pH of the solution is approximately 3.60. This corresponds to answer choice E).

User Brandon Williams
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