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Answer:
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