Is 50 ml of 15% acetic acid solution (= 1.02 g / ml) enough to dissolve 4.8 g of magnesium?

Given:
V (CH3COOH) = 50 ml
ω (CH3COOH) = 15%
ρ solution (CH3COOH) = 1.02 g / ml
m (Mg) = 4.8 g

To find:
V (CH3COOH) – Enough?

Decision:
1) 2CH3COOH + Mg => Mg (CH3COO) 2 + H2;
2) m solution (CH3COOH) = ρ solution (CH3COOH) * V solution (CH3COOH) = 1.02 * 50 = 51 g;
3) m (CH3COOH) = ω (CH3COOH) * m solution (CH3COOH) / 100% = 15% * 51/100% = 7.65 g;
4) n (CH3COOH) = m (CH3COOH) / M (CH3COOH) = 7.65 / 60 = 0.128 mol;
5) n (Mg) = m (Mg) / M (Mg) = 4.8 / 24 = 0.2 mol;
6) n must. (CH3COOH) = n (Mg) * 2 = 0.2 * 2 = 0.4 mol;
7) n (CH3COOH) <n should. (CH3COOH).

Answer: CH3COOH is not enough.