An aqueous solution containing 12.0% MgCl2 by mass has a density of 1.105g/ml. What is the mol fraction of water in this solution?
12% MgCl2 means 12 g MgCl2 in 100 g solution. Use the density to calculate the volume of 1000 mL.
1.105 g/mL x 1000 mL = 1105 grams.
1105 x 0.12 = 132.6 g MgCl2 and
1105-132.6 = ?? g H2O
moles H2O = grams/molar mass H2O
moles MgCl2 = g MgCl2/molar mass MgCl2.
XH2O = moles H2O/total moles.
Post your work if you get stuck.
Well, water you waiting for? Let's dive right into it! To find the mole fraction of water, we first need to determine the mole fraction of MgCl2 in the solution.
To do that, we'll need to calculate the amount of MgCl2 in moles. We know that the solution has a density of 1.105 g/ml, which means that 1 ml of it weighs 1.105 grams.
So, in 100 ml of the solution, you'd have 110.5 grams. Since the solution is 12.0% MgCl2 by mass, that means there are 0.12 x 110.5 grams of MgCl2 in 100 ml.
Now, we can calculate the moles of MgCl2 by dividing the mass of MgCl2 by its molar mass (95.211 g/mol) which is roughly water you get when you add an equal number of Hs and Cls together!
Next, we need to determine the amount of water in moles. Since the solution is aqueous, the remaining mass after subtracting the mass of MgCl2 is the mass of water. We can divide this mass by the molar mass of water (18.015 g/mol) to find the moles of water.
Finally, we can calculate the mole fraction of water by dividing the moles of water by the sum of the moles of both water and MgCl2.
So, water you get when you carry out this calculation is the mole fraction of water in the solution!
To find the mole fraction of water in the solution, we first need to calculate the mole fraction of MgCl2.
Step 1: Calculate the mass of MgCl2 in the solution.
Let's consider 100 g of the solution.
Mass of MgCl2 = 12.0% of 100 g = (12.0/100) * 100 g = 12 g
Step 2: Calculate the moles of MgCl2.
Molar mass of MgCl2 = (24.31 g/mol) + 2*(35.45 g/mol) = 95.21 g/mol
Moles of MgCl2 = Mass of MgCl2 / Molar mass of MgCl2 = 12 g / 95.21 g/mol = 0.126 moles
Step 3: Calculate the mass of water in the solution.
Mass of water = Total mass of the solution - Mass of MgCl2
Let's assume the total mass of the solution is 100 g.
Mass of water = 100 g - 12 g = 88 g
Step 4: Calculate the moles of water.
Molar mass of water (H2O) = (2 * 1.01 g/mol) + (16.00 g/mol) = 18.02 g/mol
Moles of water = Mass of water / Molar mass of water = 88 g / 18.02 g/mol = 4.88 moles
Step 5: Calculate the mole fraction of water.
Mole fraction of water = Moles of water / (Moles of water + Moles of MgCl2)
Mole fraction of water = 4.88 moles / (4.88 moles + 0.126 moles) = 0.976
Therefore, the mole fraction of water in the solution is 0.976.
To find the mole fraction of water in the solution, we need to determine the amount of water and the amount of MgCl2 in the solution.
Let's start by calculating the mass of water in the solution. We know that the solution has a density of 1.105 g/ml, so for every 1 ml of solution, it weighs 1.105 grams.
Since the solution contains 12.0% MgCl2 by mass, the remaining portion (100% - 12.0% = 88.0%) is the water content. Therefore, the mass of water in the solution can be calculated by multiplying 88.0% by the total mass of the solution.
Assuming we have 100 grams of solution, the mass of water can be calculated as follows:
Mass of water = 88.0% × mass of solution
Mass of water = 0.88 × 100 g
Mass of water = 88 g
Now, to calculate the amount of MgCl2 in the solution, we subtract the mass of water from the total mass of the solution.
Mass of MgCl2 = Mass of solution - Mass of water
Mass of MgCl2 = 100 g - 88 g
Mass of MgCl2 = 12 g
Next, we need to convert the mass of water and MgCl2 into moles. To do this, we divide the mass by the molar mass of each compound. The molar mass of water (H2O) is approximately 18 g/mol, and the molar mass of MgCl2 is approximately 95.21 g/mol.
Moles of water = Mass of water / molar mass of water
Moles of water = 88 g / 18 g/mol
Moles of water ≈ 4.889 mol
Moles of MgCl2 = Mass of MgCl2 / molar mass of MgCl2
Moles of MgCl2 = 12 g / 95.21 g/mol
Moles of MgCl2 ≈ 0.126 mol
Finally, we can calculate the mole fraction of water using the formula:
Mole fraction of water = Moles of water / (Moles of water + Moles of MgCl2)
Mole fraction of water = 4.889 mol / (4.889 mol + 0.126 mol)
Mole fraction of water ≈ 0.974
Therefore, the mole fraction of water in the solution is approximately 0.974.