The mole fraction of an aqueous solution of magnesium chlorate is 0.371. Calculate the molarity (in mol/L) of the magnesium chlorate solution, if the density of the solution is 1.39 g mL-1.
Take 1 mol of solution; you will have 0.371 mol Mg(ClO3)2 + 0.629 mol H2O.
.371 mol Mg(ClO3)2 x molar mass = ? g Mg(ClO3)2
0.629 mol H2O x molar mass H2O = ? g H2O
The solution consists of about 71 g Mg(ClO3)2--that's an estimate-- in 71+about 11 g H2O for a total of about 82 g. What is the volume of that?
volume = mass/density = about 82/1.39 = about 60 mL or 0.060L
You want molarity which is M = moles/L. You know mols (0.371) and you know L, that gives you M.
To calculate the molarity of the magnesium chlorate solution, we need to know the molar mass of magnesium chlorate (Mg(ClO3)2).
First, let's calculate the moles of magnesium chlorate in the solution.
Mole fraction (X) is defined as the ratio of the moles of a component to the total moles in the solution:
X = moles of magnesium chlorate / total moles in the solution
Given that the mole fraction of the solution (X) is 0.371, we can write:
0.371 = moles of magnesium chlorate / total moles in the solution
Now, let's calculate the molar mass of magnesium chlorate.
Mg(ClO3)2:
- One magnesium atom (Mg) has a molar mass of 24.31 g/mol.
- Two chlorate ions (ClO3-) contribute to the molar mass.
- One chlorate ion (ClO3-) has one chlorine atom (Cl) with a molar mass of 35.45 g/mol, and three oxygen atoms (O) with a molar mass of 3 × 16.00 g/mol.
In total, the molar mass of magnesium chlorate is:
24.31 g/mol (Mg) + 2 × (35.45 g/mol (Cl) + 3 × 16.00 g/mol (O)) = 24.31 g/mol + 106.90 g/mol = 131.21 g/mol
Now, let's calculate the moles of magnesium chlorate in the solution:
moles of magnesium chlorate = X × total moles in the solution
moles of magnesium chlorate = 0.371 × ?
moles of magnesium chlorate = 0.371 × (mass of the solution / molar mass of magnesium chlorate)
To calculate the mass of the solution, we need to use the density of the solution. Density is defined as mass per unit volume:
density = mass of the solution / volume of the solution
Rearranging the equation, we get:
mass of the solution = density × volume of the solution
Given that the density of the solution is 1.39 g/mL, and assuming a volume of 1 L (since molarity is defined per liter), we can calculate the mass of the solution:
mass of the solution = 1.39 g/mL × 1000 mL = 1390 g
Now we can substitute the values into the equation for moles of magnesium chlorate:
moles of magnesium chlorate = 0.371 × (mass of the solution / molar mass of magnesium chlorate)
moles of magnesium chlorate = 0.371 × (1390 g / 131.21 g/mol)
Calculating this expression, we find:
moles of magnesium chlorate = 3.93 mol
Finally, to calculate the molarity, we divide the moles of magnesium chlorate by the volume of the solution in liters:
molarity = moles of magnesium chlorate / volume of the solution
molarity = 3.93 mol / 1 L
Therefore, the molarity of the magnesium chlorate solution is 3.93 mol/L.
To calculate the molarity of the magnesium chlorate solution, we need to convert the given mole fraction to the moles of solute and then relate it to the volume of the solution.
Here's how you can do it:
Step 1: Calculate the moles of solute (magnesium chlorate).
The mole fraction (X) is the ratio of moles of solute to the total moles of solute and solvent:
X = moles of solute / (moles of solute + moles of solvent)
Given that the mole fraction (X) = 0.371, we can express it as:
0.371 = moles of magnesium chlorate / (moles of magnesium chlorate + moles of water)
Since we have an aqueous solution, we can assume that the moles of water (solvent) are much greater than the moles of magnesium chlorate (solute). Therefore, we can approximate the equation as:
0.371 = moles of magnesium chlorate / moles of water
Step 2: Relate the moles of solute to the volume of the solution.
To calculate the moles of solute, we need to know its molar mass. The molar mass of magnesium chlorate (Mg(ClO3)2) is 191.2 g/mol.
Step 3: Calculate the moles of solute.
moles of magnesium chlorate = X * moles of water
moles of magnesium chlorate = 0.371 * moles of water
Step 4: Calculate the volume of the solution in liters.
The density of the solution is given as 1.39 g/mL. We need to convert it to grams per liter (g/L).
1 mL = 0.001 L
density = mass / volume
1.39 g/mL = mass / volume
mass = density * volume
Assuming a volume of 1 L, we have:
mass = 1.39 g/mL * 1 L = 1.39 g
Step 5: Calculate the moles of water.
moles of water = mass of water / molar mass of water
Given that the molar mass of water (H2O) is 18.0 g/mol, we can calculate:
moles of water = 1.39 g / 18.0 g/mol
Step 6: Calculate the moles of magnesium chlorate.
moles of magnesium chlorate = 0.371 * moles of water
Step 7: Calculate the molarity of the magnesium chlorate solution.
molarity = moles of magnesium chlorate / volume of solution (in liters)
molarity = moles of magnesium chlorate / 1 liter
Substituting the calculated values, we have:
molarity = (0.371 * moles of water) / 1 liter
Simply plug in the calculated values to find the molarity of the magnesium chlorate solution.