Molarity is one of the commonly used units in chemistry. Molarity is defined as the number of moles of solute per liter of solution --- that is,
[tex]\boxed{\text{molarity} = \frac{\text{moles of solute}}{\text{volume of solution (L)}}}[/tex]
For example, a 1.46 [tex]M[/tex] glucose solution contains 1.46 mol of the solute (glucose) in 1 L of the solution. Of course, we do not always work with solution volumes of 1 L. Thus, a 500-mL solution containing 0.730 mol of glucose also has a concentration of 1.46 [tex]M.[/tex]
[tex]\\[/tex]
What is the molarity of a solution when 30 g of NaOH is mixed with 200 g of water? Density of NaOH = 2.13 g/mL; density of water = 1 g/mL.
[tex]\text{mass of solute = 30 g}[/tex]
[tex]\text{mass of solvent = 200 g}[/tex]
[tex]\text{density of solute = 2.13 g/mL}[/tex]
[tex]\text{density of solvent = 1 g/mL}[/tex]
[tex]\text{solute = NaOH}[/tex]
[tex]\text{solvent = water}[/tex]
[tex]\text{molarity}[/tex]
Step 1: Calculate the volume of solute.
[tex]\text{density of solute} = \frac{\text{mass of solute}}{\text{volume of solute}}[/tex]
[tex]\text{volume of solute} = \frac{\text{mass of solute}}{\text{density of solute}}[/tex]
[tex]\text{volume of solute} = \frac{\text{30 g}}{\text{2.13 g/mL}}[/tex]
[tex]\text{volume of solute} = \text{14.0845 mL}[/tex]
Step 2: Calculate the volume of solvent.
[tex]\text{density of solvent} = \frac{\text{mass of solvent}}{\text{volume of solvent}}[/tex]
[tex]\text{volume of solvent} = \frac{\text{mass of solvent}}{\text{density of solvent}}[/tex]
[tex]\text{volume of solvent} = \frac{\text{200 g}}{\text{1 g/mL}}[/tex]
[tex]\text{volume of solvent} = \text{200 mL}[/tex]
Step 3: Calculate the volume of solution.
volume of solution = volume of solute + volume of solvent
volume of solution = 14.0845 mL + 200 mL
volume of solution = 214.0845 mL = 0.2140845 L
Step 4: Calculate the molar mass of solute
molar mass of solute = (22.99 g/mol × 1) + (16.00 g/mol × 1) + (1.008 g/mol × 1)
molar mass of solute = 39.998 g/mol
Step 5: Calculate the number of moles of solute.
[tex]\text{moles of solute} = \frac{\text{mass of solute}}{\text{molar mass of solute}}[/tex]
[tex]\text{moles of solute} = \frac{\text{30 g}}{\text{39.998 g/mol}}[/tex]
[tex]\text{moles of solute = 0.7500375 mol}[/tex]
Step 6: Calculate the molarity of solution.
[tex]\text{molarity} = \frac{\text{moles of solute}}{\text{volume of solution (L)}}[/tex]
[tex]\text{molarity} = \frac{\text{0.7500375 mol}}{\text{0.2140845 L}}[/tex]
[tex]\boxed{\text{molarity} = 3.5 \: M}[/tex]
[tex]\\[/tex]
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