A 2.00 M solution of CaCl2 in water has a density of 1.17 g/mL. What is the mole fraction of CaCl2?
To find the mole fraction of CaCl2 in a 2.00 M solution, we first need to calculate the moles of CaCl2 present in 1 liter of the solution.
Step 1: Calculate the mass of CaCl2 in the solution:
Density = mass/volume
mass = volume x density
Given:
Density = 1.17 g/mL
Volume = 1000 mL (as 1 L = 1000 mL)
mass = 1000 mL x 1.17 g/mL
mass = 1170 g
Step 2: Calculate the moles of CaCl2:
Molar mass of CaCl2 = 40.08 g/mol (Ca=40.08 g/mol, Cl=35.45 g/mol x 2)
moles of CaCl2 = mass / molar mass
moles of CaCl2 = 1170 g / 110.98 g/mol
moles of CaCl2 = 10.53 mol
Step 3: Calculate the molality of the solution:
Molality (m) = moles of solute / mass of solvent (in kg)
Given:
Mass of solvent = 1000 g (as 1L of water = 1000 g)
moles of CaCl2 = 10.53 mol
Molality (m) = 10.53 mol / 1000 g
Molality (m) = 0.01053 mol/g
Step 4: Calculate the mole fraction of CaCl2:
The mole fraction is the ratio of moles of solute to the total moles of solute and solvent in the solution.
Mole fraction of CaCl2 = moles of CaCl2 / (moles of CaCl2 + moles of solvent)
Given:
Moles of CaCl2 = 10.53 mol
Moles of solvent = moles of water = moles of CaCl2 (as 1 mole of CaCl2 gives 1 mole of Ca2+ ions and 2 moles of Cl- ions, which means every mole of CaCl2 dissociates into 3 moles of particles in solution).
Mole fraction of CaCl2 = 10.53 mol / (10.53 mol + 10.53 mol)
Mole fraction of CaCl2 = 10.53 mol / 21.06 mol
Mole fraction of CaCl2 ≈ 0.5
Therefore, the mole fraction of CaCl2 in the 2.00 M solution is approximately 0.5.
To find the mole fraction of CaCl2 in a solution, you need to know the number of moles of CaCl2 and the total number of moles of all components in the solution.
First, let's calculate the number of moles of CaCl2 in the solution. To do that, we need to know the mass of CaCl2 dissolved in the solution.
Given:
- Solution concentration (M) = 2.00 M
- Solution density (ρ) = 1.17 g/mL
We can use the density and the volume to find the mass of the solution.
Since the density of the solution is given in grams per milliliter, we can assume that 1 mL of the solution has a mass of 1.17 grams.
Next, we need to convert the volume of the solution to moles of CaCl2. To convert volume to moles, we need to use the molar mass of CaCl2, which is approximately 110.98 g/mol.
Using the formula:
Moles = Mass / Molar mass
Moles of CaCl2 = (Density of the solution × Volume) / Molar mass
Let's calculate the moles of CaCl2:
Moles of CaCl2 = (1.17 g/mL × 1 mL) / 110.98 g/mol
Moles of CaCl2 = 0.0105 mol
Now, to calculate the total moles of all components in the solution, we can use the molarity and volume of the solution. Let's assume we have a 1 L solution for simplicity:
Total moles of all components = Molarity × Volume
Total moles of all components = 2.00 mol/L × 1 L
Total moles of all components = 2.00 mol
Finally, we can calculate the mole fraction of CaCl2 using the following formula:
Mole fraction = Moles of CaCl2 / Total moles of all components
Mole fraction = 0.0105 mol / 2.00 mol
Mole fraction ≈ 0.00525
Therefore, the mole fraction of CaCl2 in the solution is approximately 0.00525.
2.00 M CaCl2 means 2 moles CaCl2/L solution. 1 L of solution has a mass of
1.17 g/mL x 1000 mL = 1170 grams.
How much of that is water?
1170 - grams of CaCl2.
Convert grams of water to moles.
Then moles fraction CaCl2 = moles CaCl2/total moles.