# When a mixture of sodium carbonate and magnesium carbonate was calcined to constant weight, 4.48 liters of gas were released.

When a mixture of sodium carbonate and magnesium carbonate was calcined to constant weight, 4.48 liters of gas were released. The solid residue was completely reacted with 73 g of a 25% hydrochloric acid solution. Calculate the mass fraction of sodium carbonate in the original mixture. Let us write the equation for the thermal decomposition of magnesium carbonate:
MgCO3 → MgO + CO2 (1)
Thus, the solid residue is a mixture of the formed magnesium oxide and the initial sodium carbonate. Both components of the solid residue react with hydrochloric acid:
MgO + 2HCl → MgCl2 + H2O (2)
Na2CO3 + 2HCl → MgCl2 + CO2 ↑ + H2O (3)
Let us calculate the amount of substance released by CO2 released during the decomposition of MgCO3:
n (CO2) = 4.48 L / 22.4 L / mol = 0.2 mol.
From equation (1): n (MgO) = n (CO2) = 0.2 mol,
m (MgO) = n (MgO) ∙ M (MgO) = 0.2 mol ∙ 40 g / mol = 8 g.
Let’s find the amount of hydrochloric acid substance required for the reaction with MgO:
n (HCl) 2 = 2 ∙ n (MgO) = 2 ∙ 0.2 mol = 0.4 mol.
Let’s find the total mass and amount of the hydrochloric acid substance taken for the reaction:
m (HCl (total)) in-islands = m (HCl (total)) solution ∙ ω (HCl) = 73 g ∙ 0.25 = 18.25 g,
n (HCl (gen.)) = m (HCl (gen.)) in islands / M (HCl) = 18.25 g / 36.5 g / mol = 0.5 mol.
Let’s find the amount of hydrochloric acid substance required for the reaction with Na2CO3:
n (HCl) 3 = n (HCl (gen.)) – n (HCl) 2 = 0.5 mol – 0.4 mol = 0.1 mol.
Find the amount of substance and the mass of sodium carbonate in the original mixture.
From equation (3): n (Na2CO3) = 0.5 ∙ n (HCl) 3 = 0.5 ∙ 0.1 mol = 0.05 mol.
m (Na2CO3) = n (Na2CO3) ∙ M (Na2CO3) = 0.05 mol, ∙ 106 g / mol = 5.3 g.
Let’s find the amount of substance and the mass of magnesium carbonate in the initial mixture.
From equation (1): n (MgCO3) = n (CO2) = 0.2 mol,
m (MgCO3) = n (MgCO3) ∙ M (MgCO3) = 0.2 mol ∙ 84 g / mol = 16.8 g.
Determine the mass of the initial mixture and the mass fraction of sodium carbonate in it:
m (MgCO3 + Na2CO3) = m (MgCO3) + m (Na2CO3) = 16.8 g + 5.3 g = 22.1 g.
ω (Na2CO3) = m (Na2CO3) / m (MgCO3 + Na2CO3) = 5.3 g / 22.1 g = 0.24 (24%). Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.