A 2.00 M solution of calcium choloride in water has a density of 1.17g/mL. What is the mole fraction of calcium chloride?
How do I solve this? I know that density=mass/volume. The mm of calcium chloride is 111g/mol. I don't know how to connect this information.
2.00 M = 2.00 mols/Liter of solution.
Convert 2.00 M to grams CaCl2 in the solution.
1 L of the solution has a mass of 1.17 x 1000. That is the mass of the water + the mass of the CaCl2.
Subtract mass CaCl2 to obtain mass H2O.
Now you have the mass and # mols CaCl2 and the mass of H2O.
Can you go from here?
mol fraction X = molsX/(mols x + mols y)
To solve this problem, you need to use the relationship between concentration, density, and molar mass.
First, let's convert the given density from grams per milliliter (g/mL) to grams per liter (g/L). Since there are 1000 mL in a liter, the density can be expressed as 1.17 g/mL * 1000 mL/L = 1170 g/L.
Next, we can use the definition of molarity (M) to find the moles of calcium chloride present in 1 liter of the solution. The molarity is defined as the number of moles of solute divided by the volume of the solution in liters. In this case, the molarity is given as 2.00 M, which means there are 2.00 moles of calcium chloride in 1 liter of the solution.
Therefore, the mass of calcium chloride in the solution can be calculated by multiplying the moles of calcium chloride by its molar mass. The molar mass of calcium chloride is given as 111 g/mol. So, the mass of calcium chloride in the solution is 2.00 M * 111 g/mol = 222 g/L.
Now that we have the mass of calcium chloride in the solution (222 g/L) and the total mass of the solution (1170 g/L), we can calculate the mole fraction.
The mole fraction (X) of a component in a solution is defined as the moles of that component divided by the total moles of all components. In this case, the moles of calcium chloride is given as 2.00 moles, and the total moles can be calculated by dividing the mass of the solution by its molar mass.
The total moles of the solution can be found by dividing the mass of the solution by its molar mass, which is 1170 g/L / (18 g/mol for water + 111 g/mol for calcium chloride) = 1170 g/L / 129 g/mol = 9.07 mol/L.
Finally, the mole fraction of calcium chloride (XCaCl2) can be calculated as 2.00 moles / 9.07 moles = 0.22.
Therefore, the mole fraction of calcium chloride in the solution is 0.22.