Question

The ionization constant of lactic acid, (CH₃CH(OH)CO₂H) ((Kₐ = 1.36 × 10^−4)). If 20.0 g of lactic acid is used to make a solution with a volume of 1.00 L, what is the concentration of hydronium ion in the solution?

a) 1.36 × 10⁻4 , M
b) 2.72 × 10⁻4 , M
c) 5.44 × 10⁻4 , M
d) 1.08 × 10⁻3, M

Answer 1

The concentration of hydronium ion
`(\(H_3O^+\))` in the solution is approximately
`\(5.44 * 10^(-4) \, \text{M}\).` Therefore, the correct answer is option
`(c) \(5.44 * 10^(-4) \, \text{M}\).`

Step-by-step explanation:

To determine the concentration of hydronium ion
`(\(H_3O^+\))` in the solution, we can use the ionization constant
`(\(K_a\))` of lactic acid. The balanced chemical equation for the ionization of lactic acid is:

`\[ \text{CH}_3\text{CH(OH)CO}_2\text{H} \rightleftharpoons \text{CH}_3\text{CH(OH)CO}_2^- + \text{H}_3\text{O}^+ \]`

Given that the ionization constant
`(\(K_a\))` is
`\(1.36 * 10^(-4)\)`, we can set up an ICE (initial, change, equilibrium) table for the ionization reaction:

`\[\begin{array}{cccc}& \text{CH}_3\text{CH(OH)CO}_2\text{H} & \rightleftharpoons & \text{CH}_3\text{CH(OH)CO}_2^- & + & \text{H}_3\text{O}^+ \\\text{Initial (M)} & x & & 0 & & 0 \\\text{Change (M)} & -x & & +x & & +x \\\text{Equilibrium (M)} & x & & x & & x \\\end{array}\]`

The ionization constant
`(\(K_a\))` is given by the expression:

`\[ K_a = \frac{\text{[CH}_3\text{CH(OH)CO}_2^-]\text{[H}_3\text{O}^+]}{\text{[CH}_3\text{CH(OH)CO}_2\text{H}]} \]`

Substitute the equilibrium concentrations into the
`\(K_a\)` expression:

`\[ 1.36 * 10^(-4) = (x * x)/(0.020 - x) \]`

Since
`\(x\)` is expected to be small compared to 0.020, we can approximate
`\(0.020 - x\) as 0.020. Solve for \(x\):`

`\[ x^2 = 1.36 * 10^(-4) * 0.020 \]`

`\[ x = \sqrt{1.36 * 10^(-4) * 0.020} \]`

`\[ x \approx 5.44 * 10^(-4) \, \text{M} \]`

So, the concentration of hydronium ion
`(\(H_3O^+\))` in the solution is approximately
`\(5.44 * 10^(-4) \, \text{M}\).` Therefore, the correct answer is option
`(c) \(5.44 * 10^(-4) \, \text{M}\).`