You dissolved 450.0 g of sugar (C12H22O11) in 150 mL of water. The density of water is 1.00
g/mL
a. calculate the molarity of the solution
b. calculate the molality of the solution
To calculate the molarity (M) of the solution, we need to determine the number of moles of solute (sugar) dissolved in the given volume of water.
a. To find the molarity, we can use the formula:
M = moles of solute / volume of solution in liters
First, we need to convert the grams of sugar to moles. We can do this by using the molar mass of sugar, which is the sum of the atomic masses of its elements.
Molar mass of sugar (C12H22O11):
(12.01 g/mol x 12) + (1.01 g/mol x 22) + (16.00 g/mol x 11) = 342.34 g/mol
Now, we can calculate the moles of sugar:
moles of sugar = mass of sugar / molar mass of sugar
= 450.0 g / 342.34 g/mol
= 1.313 mol
Next, we need to convert the volume of water from milliliters to liters:
volume of solution = 150 mL = 150 / 1000 L = 0.150 L
Finally, we can plug these values into the molarity formula:
M = 1.313 mol / 0.150 L
≈ 8.75 M
Therefore, the molarity of the solution is approximately 8.75 M.
b. The molality (m) of a solution is calculated by dividing the moles of solute by the mass of the solvent (water) in kilograms.
First, let's convert the mass of water from grams to kilograms:
mass of water = volume of water x density of water
= 150 mL x 1.00 g/mL
= 150 g
mass of water = 150 g / 1000 g/kg
= 0.150 kg
Next, we can calculate the molality using the formula:
m = moles of solute / mass of solvent in kilograms
m = 1.313 mol / 0.150 kg
≈ 8.75 m
Therefore, the molality of the solution is approximately 8.75 m.