The mixture contains K₂CO₃ and KCl. But only K₂CO₃ reacts with HCl and produces KCl, H₂O and CO₂ as the products.
The balanced reaction equation is
K₂CO₃(s) + 2HCl(aq) → 2KCl(aq) + H₂O(l) + CO₂ (g)
Molarity (M) = moles of solute (mol) / Volume of the solution (L)
Molarity of HCl = 0.01M
Volume of added HCl = 40.00 x 10⁻³ L
Hence,
moles of HCl = Molarity x Volume of the solution
= 0.01M x 40.00 x 10⁻³ L
= 4 x 10⁻⁴ mol
The stoichiometric ratio between K₂CO₃ and HCl is 1 : 2.
Hence,
moles of K₂CO₃ in 25.00 mL of Solution = moles of reacted HCl / 2
= (4 x 10⁻⁴ mol) / 2
= 2 x 10⁻⁴ mol
moles of K₂CO₃ in 25.00 mL = 2 x 10⁻⁴ mol
moles of K₂CO₃ in 250.00 mL = (2 x 10⁻⁴ mol x 250.00 mL) / 25.00 mL
= 2 x 10⁻³ mol
Hence, moles of K₂CO₃ in the mixture = 2 x 10⁻³ mol
Moles (mol) = Mass (g) / Molar mass (g/mol)
Molar mass of K₂CO₃ = (39 x 2 + 12 + 16 x 3) g/mol
= 138 g/mol
Mass of K₂CO₃ = moles x molar mass
= 2 x 10⁻³ mol x 138 g/mol
= 0.276 g
K₂CO₃ (w/w %) = (mass of K₂CO₃ / total mass of mixture) x 100 %
= (0.276 g / 3.0 g) x 100 %
= 9.2 %
Hence, the answer is 9.2 %.
