What volume of sodium hydroxide solution with a mass fraction of 5.5% (density 1.06 g / ml)

What volume of sodium hydroxide solution with a mass fraction of 5.5% (density 1.06 g / ml) is required to neutralize the acid obtained by the oxidation of 4.4 g of ethanal?

Given:
ω (NaOH) = 5.5%
p (solution) = 1.06 ml
m (ethanal) = 4.4 g
To find:
V (solution NaOH) -?
Decision:
Let us write down the reaction equations mentioned in the problem.
5CH3-CHO + 2KMnO4 + 3H2SO4 = 2MnSO4 + K2SO4 + 3H2O + 5CH3-COOH (1)
C (+1) – 2e -> C (+3) – reducing agent | five
Mn (+7) + 5e -> C (+2) – oxidizing agent | 2
CH3-COOH + NaOH -> CH3-COONa + H2O (2)
n (ethanal) = m / M = 4.4 / 44 mol = 0.1 mol.
According to the reaction equation 1, n (acetic acid) = n (ethanal) = 0.1 mol.
According to the equation 2, n (NaOH) = n (acetic acid) = 0.1 mol.
m (pure NaOH) = M × n = 0.1 × 40 g = 4 g.
We found the mass of NaOH in the solution and we can find the mass of the solution itself.
ω (in-va) = m (in-va) / m (solution) × 100%
Then m (NaOH solution) = m (pure NaOH) / 0.01ω = 4 / 0.055 g = 72.73 g.
p = m / V. Hence V = m / p.
V (solution of NaOH) = 72.73 g / 1.06 ml = 68.613 ml.
Answer: 68.613 ml.