3. How many grams of NaCl must be dissolved in 100. g of water to make a solution of 3.46 m in NaCl?
4. A solution is prepared by mixing 16.0 g of CH3OH and 50.0 g of water.
(a) What is the mass percent of methanol in the solution?
(b) what is the mole fraction of each component in the solution?
(c) If the density of solution is 0.955 g/mL, what is the molarity and molality of CH3OH, respectively, in the solution?
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Answer:
3. To find the grams of NaCl needed, we need to use the formula:
molarity (M) = moles of solute / liters of solution
First, we need to calculate the moles of NaCl:
3.46 mol/L = moles of NaCl / 1 L
moles of NaCl = 3.46 mol/L
Next, we need to convert the moles of NaCl to grams:
moles of NaCl = (mass of NaCl in grams) / (molar mass of NaCl)
mass of NaCl in grams = (moles of NaCl) x (molar mass of NaCl)
The molar mass of NaCl is 58.44 g/mol.
mass of NaCl in grams = (3.46 mol/L) x (58.44 g/mol) = 202.21 g/L
To make a 3.46 M solution, we would need 202.21 g of NaCl per liter of solution. Since we want to make a 100. g solution, we will need to use a proportion:
202.21 g / L = x g / 0.1 L
x = 20.22 g
Therefore, we need 20.22 g of NaCl to dissolve in 100. g of water to make a 3.46 m solution.
4.
(a) Mass percent of CH3OH:
mass percent = (mass of solute / mass of solution) x 100%
mass of solute = 16.0 g CH3OH
mass of solution = 16.0 g CH3OH + 50.0 g water = 66.0 g
mass percent of CH3OH = (16.0 g / 66.0 g) x 100% = 24.2%
(b) Mole fraction of CH3OH:
Mole fraction = (moles of component / total moles in solution)
First, we need to calculate the moles of CH3OH:
moles of CH3OH = 16.0 g / (32.04 g/mol) = 0.499 mol
Next, we need to calculate the moles of water:
moles of H2O = 50.0 g / (18.02 g/mol) = 2.777 mol
Total moles in solution = moles of CH3OH + moles of H2O = 3.276 mol
Mole fraction of CH3OH = 0.499 mol / 3.276 mol = 0.152
Mole fraction of H2O = 2.777 mol / 3.276 mol = 0.848
(c) Molarity and molality of CH3OH:
Molarity (M) = moles of solute / liters of solution
moles of CH3OH = 0.499 mol
liters of solution = (16.0 g + 50.0 g) / (0.955 g/mL) = 66.49 mL = 0.06649 L
Molarity of CH3OH = 0.499 mol / 0.06649 L = 7.50 M
Molality (m) = moles of solute / kilograms of solvent
moles of CH3OH = 0.499 mol
kilograms of solvent = 50.0 g / 1000 g/kg = 0.0500 kg
Molality of CH3OH = 0.499 mol / 0.0500 kg = 9.98 m