A CaCO3 mixture weighing 2.75 grams was treated with 9.75 mL of 3.00 M HCl to liberate CO2. After the CO2 was liberated, the mass of the mixture decreased to 2.621 grams. Determine the mass of CaCO3 present in the mixture.
Loss in mass = mass CO2 = 2.621g.
mols CO2 = grams CO2/molar mass CO2.
mols CaCO3 = mols CO2 (look at the balanced equation).
CaCO3 ==> CaO + CO2.
g CaCO3 = mols CaCO3 x molar mass CaCO3.
To determine the mass of CaCO3 present in the mixture, we need to calculate the mass of CO2 that was liberated when the mixture was treated with HCl. Then we can determine the mass of CaCO3 by subtracting the mass of CO2 from the initial mass of the mixture.
1. Calculate the moles of HCl used:
- Given the volume of HCl used (9.75 mL) and its concentration (3.00 M), we can calculate the number of moles of HCl by using the formula: moles = concentration * volume / 1000.
- Convert the volume to liters: 9.75 mL = 9.75/1000 = 0.00975 L.
- Calculate the moles of HCl: moles HCl = 3.00 M * 0.00975 L = 0.02925 mol.
2. Write a balanced chemical equation for the reaction between HCl and CaCO3:
CaCO3 + 2HCl -> CaCl2 + H2O + CO2.
According to the stoichiometry of the reaction, it takes 1 mole of CaCO3 to liberate 1 mole of CO2.
3. Calculate the number of moles of CO2 liberated:
- Since the mole ratio between CaCO3 and CO2 is 1:1, the number of moles of CO2 will be the same as the number of moles of CaCO3 used.
- Moles of CO2 = moles of CaCO3 = 0.02925 mol.
4. Calculate the mass of CO2 liberated:
- Given that the molar mass of CO2 is 44.01 g/mol, we can calculate the mass of CO2 by multiplying the number of moles of CO2 by its molar mass.
- Mass of CO2 = moles of CO2 * molar mass of CO2 = 0.02925 mol * 44.01 g/mol = 1.282 g.
5. Calculate the mass of CaCO3:
- Subtract the mass of CO2 (1.282 g) from the initial mass of the mixture (2.75 g):
- Mass of CaCO3 = Initial mass of mixture - Mass of CO2 = 2.75 g - 1.282 g = 1.468 g.
Therefore, the mass of CaCO3 present in the mixture is 1.468 grams.