A 6.3% nitric acid solution was used to dissolve barium carbonate. The resulting gas was completely absorbed

A 6.3% nitric acid solution was used to dissolve barium carbonate. The resulting gas was completely absorbed by the calcium hydroxide solution, and 20 grams of precipitate were formed. How many grams of nitric acid solution was spent?

Let’s write down the reaction equations:
ВaCO3 + 2HNO3 = Ba (NO3) 2 + H2O + CO2 ↑
CO2 + Ca (OH) 2 = CaCO3 ↓ + H2O
Let’s start with the second equation:
It can be seen from the reaction equation that:
ν (CaCO3) = ν (CO2)
m (CaCO3) / M (CaCO3) = V (CO2) / Vm (CO2)
Determine the molar mass of calcium carbonate:
M (CaCO3) = 40 + 12 + 16 * 3 = 100 g / mol
Determine the volume of carbon dioxide by expressing from the equation:
V (CO2) = m (CaCO3) * Vm (CO2) / M (CaCO3)
Substitute the numerical values:
V (CO2) = m (CaCO3) * Vm (CO2) / M (CaCO3) = 20 * 22.4 / 100 = 4.48 liters.
Now let’s move on to the first reaction:
It can be seen from the reaction equation that:
ν (HNO3) / 2 = ν (CO2)
m (HNO3) / 2 * M (HNO3) = V (CO2) / Vm (CO2)
Determine the molar mass of nitric acid:
M (HNO3) = 1 + 4 + 16 * 3 = 63 g / mol
Determine the mass of nitric acid by expressing from the equation:
m (HNO3) = 2 * M (HNO3) * V (CO2) / Vm (CO2)
Substitute the numerical values:
m (HNO3) = 2 * M (HNO3) * V (CO2) / Vm (CO2) = 2 * 63 * 4.48 / 22.4 = 25.2 g.
m (solution) = m (HNO3) * 100% / w (HNO3) = 25.2 * 100 / 6.3 = 400 g.
Answer: the mass of the acid solution is 400 g.