I cannot figure out this problem. It says to "Calculate the mole fraction of MgCl2 (subscript 2) in a solution created by dissolving 132.1 g of MgCl2 in 175 mL of water."
I started by converting 132.1g to moles, but I got stuck when I tried to convert 175mL to moles.
For reference, the answer given in the back of the book is 0.125
You started correctly.
mols MgCl2 = grams/molar mass = ?
mols H2O = grams H2O/molar mass H2O. We assume that the density of H2O is 1 g/mL so 175 mL H2O has a mass of 175 g.
total mols then is mols MgCl2 + mols H2O.
I assume you know how to do the remainder.
To convert 175 mL of water to moles, you need to use the density and molar mass of water.
1. Start by converting the volume of water from milliliters (mL) to grams (g) using the density of water, which is 1 g/mL.
Mass of water = Volume of water x Density of water
Mass of water = 175 mL x 1 g/mL
Mass of water = 175 g
2. Next, convert the mass of water to moles using the molar mass of water, which is approximately 18.015 g/mol.
Moles of water = Mass of water / Molar mass of water
Moles of water = 175 g / 18.015 g/mol
Moles of water ≈ 9.715 mol
Now that you have calculated the moles of both MgCl2 (from the given mass) and water, you can find the mole fraction of MgCl2.
3. To find the mole fraction of MgCl2, divide the moles of MgCl2 by the total moles of the solution (MgCl2 + water).
Moles of MgCl2 = Mass of MgCl2 / Molar mass of MgCl2
Moles of MgCl2 = 132.1 g / (24.305 g/mol + 35.453 g/mol x 2)
Moles of MgCl2 ≈ 1.624 mol
Total moles of the solution = Moles of MgCl2 + Moles of water
Total moles of the solution ≈ 1.624 mol + 9.715 mol
Total moles of the solution ≈ 11.339 mol
Mole fraction of MgCl2 = Moles of MgCl2 / Total moles of the solution
Mole fraction of MgCl2 ≈ 1.624 mol / 11.339 mol
Mole fraction of MgCl2 ≈ 0.143
Therefore, the mole fraction of MgCl2 in the solution is approximately 0.143, which is not the same as the answer given in the book (0.125). Double-check your calculations to ensure accuracy.
To calculate the mole fraction of MgCl2 in the solution, you need to first convert the mass of MgCl2 to moles, and then convert the volume of water to moles. Here's how to do that step-by-step:
1. Convert the mass of MgCl2 to moles:
You already started this step, so let's continue. The molar mass of MgCl2 can be calculated by summing the atomic masses of magnesium (Mg) and chlorine (Cl):
Mg: 1 atom * 24.31 g/mol = 24.31 g/mol
Cl: 2 atoms * 35.45 g/mol = 70.90 g/mol
Total molar mass of MgCl2 = 24.31 + 70.90 = 95.21 g/mol (approximately)
To convert the mass of MgCl2 to moles, divide the given mass (132.1 g) by the molar mass (95.21 g/mol):
132.1 g / 95.21 g/mol ≈ 1.3871 mol MgCl2
So, you correctly determined that there are approximately 1.3871 moles of MgCl2.
2. Convert the volume of water to moles:
To convert the volume of water to moles, you need to use the density of water and its molar volume.
The density of water is approximately 1 g/mL. Therefore, the mass of 175 mL of water is:
175 mL * 1 g/mL = 175 g
Now you can convert these grams of water to moles by dividing by the molar mass of water. The molar mass of water (H2O) is approximately 18.02 g/mol:
175 g / 18.02 g/mol ≈ 9.7169 mol water
So, there are approximately 9.7169 moles of water.
3. Calculate the mole fraction of MgCl2:
To calculate the mole fraction of MgCl2, you need to divide the number of moles of MgCl2 by the total number of moles in the solution (which is the sum of moles of MgCl2 and moles of water).
Mole fraction of MgCl2 = moles of MgCl2 / (moles of MgCl2 + moles of water)
Mole fraction of MgCl2 = 1.3871 mol / (1.3871 mol + 9.7169 mol) ≈ 0.125
So, the mole fraction of MgCl2 in the solution is approximately 0.125.
The given answer of 0.125 confirms that your calculations were correct.