Answer to Question #112154 in Chemistry for Cassandra Valdez

Question

A solution is prepared by dissolving 3.50g of sodium hydroxide in water and adding water until the volume of the solution is 2.50L. What are the OH- and H3O+ concentrations?Write your answer using OH- and H3O+ identifying which you are calculating reporting three significant figures.

Answer 1

Solution:

1) Molar mass of sodium hydroxide (NaOH) is 40 g/mol.

Molar mass is the mass of one mole of a substance. Therefore,

Moles of NaOH = Mass of NaOH / Molar mass of NaOH.

n(NaOH) = (3.50 g) / (40 g/mol) = 0.0875 mol.

n(NaOH) = 0.0875 mol.

2) Molarity is the number of moles of solute per liter of solution. Therefore,

Molarity of NaOH = Moles of NaOH / Volume of solution.

C(NaOH) = (0.0875 mol) / (2.50 L) = 0.0350 M.

C(NaOH) = 0.035 M.

3) NaOH is a highly soluble salt and will fully dissociate in aqueous solution to produce equivalent molarity of sodium cation and hydroxide anion:

NaOH(s) → Na⁺(aq) + OH⁻(aq)

C(NaOH) = [Na⁺] = [OH⁻] = 0.0350 M.

[OH⁻] = 0.0350 M.

The concentration of OH⁻ is 0.0350 M.

4) The concentrations of hydronium (H₃O⁺) and hydroxide (OH⁻) ions are related together through the auto-ionization equlibrium constant (K_w):

K_w = [H₃O⁺] × [OH⁻] = 10^-14

Therefore,

[H₃O⁺] = K_w / [OH⁻];

[H₃O⁺] = (10^-14) / (0.035) = 2.857×10^-13 M = 2.86×10^-13 M.

[H₃O⁺] = 2.86×10^-13 M.

The concentration of H₃O⁺ is 2.86×10^-13 M.

Answer:

[OH⁻] = 0.0350 M;

[H₃O⁺] = 2.86×10^-13 M.