If 12.90 mL of a 18.2 Weight% solution of sodium chloride is diluted to a final volume of 3.00 liters, what is the Molar concentration of the diluted solution? The density of the original solution is 1.12 g/mL.
To find the molar concentration of the diluted solution, we first need to calculate the number of moles of sodium chloride present in the 12.90 mL of the original solution.
Step 1: Calculate the mass of sodium chloride in the 12.90 mL of the original solution.
Mass of original solution = Volume × Density
Mass of original solution = 12.90 mL × 1.12 g/mL
Step 2: Calculate the mass of sodium chloride in the original solution.
Weight% = (Mass of solute / Mass of solution) × 100
18.2 = (Mass of sodium chloride / Mass of original solution) × 100
Rearranging the equation, we get:
Mass of sodium chloride = (18.2 / 100) × Mass of original solution
Step 3: Calculate the moles of sodium chloride.
Moles = Mass / Molecular Weight
Moles of sodium chloride = Mass of sodium chloride / Molecular Weight
Step 4: Calculate the molar concentration.
Molar concentration = Moles / Volume of diluted solution
Now let's plug in the values and calculate the molar concentration:
Step 1:
Mass of original solution = 12.90 mL × 1.12 g/mL
Mass of original solution = 14.448 g
Step 2:
Mass of sodium chloride = (18.2 / 100) × Mass of original solution
Mass of sodium chloride = (18.2 / 100) × 14.448 g
Mass of sodium chloride = 2.630896 g
Step 3:
Moles of sodium chloride = Mass of sodium chloride / Molecular Weight
Since the molecular weight of sodium chloride is 58.44 g/mol,
Moles of sodium chloride = 2.630896 g / 58.44 g/mol
Moles of sodium chloride = 0.04501 mol
Step 4:
Molar concentration = Moles / Volume of diluted solution
Volume of diluted solution = 3.00 liters
Molar concentration = 0.04501 mol / 3.00 L
Molar concentration = 0.015 M
Therefore, the molar concentration of the diluted solution is 0.015 M.