To find the percent by mass of CaCl2 2H2O in the salt mixture, we need to determine the moles of CaCl2 2H2O and the total moles of the salt mixture.
1. Determine the moles of CaCl2 2H2O:
- The molar mass of CaCl2 2H2O is calculated as follows:
- Molar mass of Ca = 40.08 g/mol
- Molar mass of Cl2 = 2 * 35.45 g/mol = 70.90 g/mol
- Molar mass of 2H2O = 2 * (2 * 1.01 g/mol + 16.00 g/mol) = 36.04 g/mol
- Therefore, the molar mass of CaCl2 2H2O = 40.08 g/mol + 70.90 g/mol + 36.04 g/mol = 146.02 g/mol
- We have a sample of 0.375 g of the precipitate. Let's convert this to moles:
- Moles of CaCl2 2H2O = mass / molar mass = 0.375 g / 146.02 g/mol = 0.002566 mol
2. Determine the total moles of the salt mixture:
- We know the mass of the CaCl2 2H2O + H2O mixture is 0.972 g.
- Let's subtract the mass of the precipitate to find the mass of the remaining H2O:
- Mass of H2O = Mass of mixture - Mass of precipitate = 0.972 g - 0.375 g = 0.597 g
- We can now calculate the moles of H2O:
- Moles of H2O = mass / molar mass = 0.597 g / 18.02 g/mol = 0.0331 mol
3. Calculate the moles of CaCl2 2H2O in the original mixture:
- Subtract the moles of H2O from the total moles of the mixture:
- Moles of CaCl2 2H2O = Total moles - Moles of H2O = 0.002566 mol - 0.0331 mol = -0.0305 mol
(Note: The negative sign indicates that there is not enough CaCl2 2H2O to fully react. It is the limiting reactant.)
4. Find the percent by mass of CaCl2 2H2O in the salt mixture:
- To do this, we need to determine the mass of the salt mixture.
- Mass of salt mixture = Mass of precipitate + Mass of H2O = 0.375 g + 0.597 g = 0.972 g
- Calculate the percent by mass of CaCl2 2H2O:
- Percent by mass of CaCl2 2H2O = (Moles of CaCl2 2H2O / Total moles) × 100
- Percent by mass of CaCl2 2H2O = (0.002566 mol / (0.002566 mol - 0.0331 mol)) × 100
- Percent by mass of CaCl2 2H2O ≈ 7.6% (rounded to one decimal place)
Therefore, the percent by mass of CaCl2 2H2O in the salt mixture is approximately 7.6%.