What mass of NaOH would need to be dissolved in 500.0 mL of water to produce a solution with a pH of 12.40

0.5024 g

Explanation:

Step 1: Calculate the concentration of H⁺

We will use the definition of pH.

pH = -log [H⁺]

[H⁺] = antilog -pH = antilog -12.40 = 3.981 × 10⁻¹³ M

Step 2: Calculate the concentration of OH⁻

We will use the ionic product of water expression.

[H⁺] [OH⁻] = 10⁻¹⁴

[OH⁻] = 10⁻¹⁴/[H⁺] = 10⁻¹⁴/3.981 × 10⁻¹³ = 0.02512 M

Step 3: Calculate the initial concentration of NaOH

NaOH is a strong base and the molar ratio of NaOH to OH⁻is 1:1. Thus, the initial concentration of NaOH is 1/1 × 0.02512 M = 0.02512 M.

Step 4: Calculate the moles of NaOH

We will use the definition of molarity.

M = moles of NaOH/liters of solution

moles of NaOH = M × liters of solution

moles of NaOH = 0.02512 mol/L × 0.5000 L = 0.01256 mol

Step 5: Calculate the mass of 0.01256 moles of NaOH

The molar mass of NaOH is 40.00 g/mol.

0.01256 mol × 40.00 g/mol = 0.5024 g