How many grams of CaCl2 * 6H2O are required to make 500 milliliters of a solution having the same concentration of Cl- as one that was prepared by dissolving 75.6 grams of NaCl in enough water to make exactly 1 liter of solution?
To find the number of grams of CaCl2 * 6H2O required to make a solution with the same concentration of Cl- as the NaCl solution, we need to consider the molar mass and stoichiometry.
1. Find the molar mass of NaCl:
- The molar mass of NaCl is the sum of the atomic masses of sodium (Na) and chlorine (Cl).
- Na: 22.99 g/mol
- Cl: 35.45 g/mol
- Molar mass of NaCl: 22.99 + 35.45 = 58.44 g/mol
2. Calculate the number of moles of NaCl used:
- Given mass of NaCl: 75.6 g
- Moles of NaCl = mass / molar mass = 75.6 g / 58.44 g/mol ≈ 1.295 mol
3. Determine the number of moles of Cl- ions in the NaCl solution:
- NaCl dissociates into one Na+ ion and one Cl- ion.
- Therefore, the number of moles of Cl- ions is the same as the moles of NaCl, which is 1.295 mol.
4. Convert 500 mL to liters:
- 500 mL ÷ 1000 mL/L = 0.5 L
5. Use the stoichiometry of CaCl2 * 6H2O:
- The compound CaCl2 * 6H2O has two Cl- ions per formula unit.
- Therefore, the number of moles of CaCl2 * 6H2O required to have the same concentration of Cl- ions is 1.295 mol Cl- ions / 2 = 0.6475 mol CaCl2 * 6H2O.
6. Calculate the mass of CaCl2 * 6H2O required:
- To find the mass, we need the molar mass of CaCl2 * 6H2O.
- Ca: 40.08 g/mol
- Cl: 35.45 g/mol
- O: 16.00 g/mol
- H: 1.01 g/mol
- Molar mass of CaCl2 * 6H2O = (40.08 + 2 * 35.45 + 6 * (1.01 + 16.00)) g/mol = 219.08 g/mol
- Mass of CaCl2 * 6H2O = moles * molar mass = 0.6475 mol * 219.08 g/mol ≈ 141.89 g
Therefore, approximately 141.89 grams of CaCl2 * 6H2O are required to make 500 milliliters of a solution with the same concentration of Cl- as one prepared by dissolving 75.6 grams of NaCl in enough water to make exactly 1 liter of solution.