Find the mass of a potassium hydroxide solution with a mass fraction of alkali of 4% required for the reaction with carbon dioxide

Find the mass of a potassium hydroxide solution with a mass fraction of alkali of 4% required for the reaction with carbon dioxide, if the result is a salt with a mass of 27.6 g.

2KOH + CO2 = K2CO3 + H2O
n (K2CO3) = m / M = 27.6 / 138 = 0.2 mol
from the reaction equation follows: n (KOH) = n (K2CO3) x2 = 0.2×2 = 0.4 mol
m (KOH) = nxM = 0.4×56 = 22.4 grams
m (KOH p-p) = m (KOH) / W (p-pa) = 22.4 / 0.04 = 560 grams