Answer to Question #312145 in Chemistry for Boyly

Question

What weight of lactic acid must be dissolved in a liter of solution to produce a hydronium-ion concentration of 1×10^-5

Answer 1

Solution:

lactic acid = CH₃CH(OH)COOH

hydronium ion = H₃O⁺

Lactic acid (CH₃CH(OH)COOH) is a weak acid because it partially dissociates in an aqueous solution or it does not ionize completely in solution to produce hydronium ions (H₃O⁺).

Equation representing the dissociation of CH₃CH(OH)COOH:

CH₃CH(OH)COOH(aq) + H₂O(l) ⇋ H₃O⁺(aq) + CH₃CH(OH)COO⁻(aq)

CH₃CH(OH)COOH = HA

CH₃CH(OH)COO⁻ = A⁻

ICE Table:

According to the ICE Table:

[H₃O⁺] = [CH₃CH(OH)COO⁻] = 1×10⁻⁵

[CH₃CH(OH)COOH] = C − 1×10⁻⁵

The K_a expression for the dissociation of CH₃CH(OH)COOH:

K_a = 1.4×10⁻⁴ (for lactic acid )

Therefore,

1.4×10⁻⁴ = [1×10⁻⁵] × [1×10⁻⁵] / [C − 1×10⁻⁵]

7.14×10⁻⁷ = C − 1×10⁻⁵

C = 1.07×10⁻⁵

Molarity of lactic acid = 1.07×10⁻⁵ M

Moles of lactic acid = Molarity of lactic acid × Liters of solution

Therefore,

Moles of lactic acid = (1.07×10⁻⁵ M) × (1 L) = 1.07×10⁻⁵ mol

The molar mass of lactic acid (CH₃CH(OH)COOH) is 90.08 g/mol

Therefore,

Mass of lactic acid = (1.07×10⁻⁵ mol) × (90.08 g/mol) = 9.64×10⁻⁴ g

Mass of lactic acid = 9.64×10⁻⁴ g

Answer: 9.64×10⁻⁴ grams of lactic acid must be dissolved