8.3 Concentration of solutions

Concentration – amount of solute per quantity of solvent Ways to express the concentration of a solution Concentration as a Mass/Volume Percent Concentration as a Mass/Mass Percent Concentration as a Volume/Volume Percent Parts per million/billion Molar Concentration

Concentration as a Mass/Mass percent Mass/mass percent gives the mass of a solute divided by the mass of a solution also referred to as percent (m/m) Mass/mass percent = x 100 % Mass of solute (in g) Mass of solution (in g)

Mass of solute (in g) Mass/mass percent = x 100% Calcium chloride can be used instead of road salt to melt the ice on roads during the winter. To determine how much calcium chloride had been used on a road, a student took a sample of slush to analyze. The sample had a mass of 23.47 g. When the solution was evaporated, the residue had a mass of 4.58 g. What was the mass/mass percent of calcium chloride in the slush? Mass of solute (in g) Mass of solution (in g) Mass/mass percent = x 100% = x 100% = 4.58 g 23.47 g 19.5 % The mass/mass percent was 19.5% (m/m) 19.5 g of calcium chloride was dissolved in 100 g of solution

Molar Concentration

Molarity is the number of moles of solute that can dissolve in 1 L of solution. Molar concentration (mol/L) = Amount of solute (mol) Volume of solution (L) n C = V

Step 1: Find the number of moles of calcium chloride using n=m/M n= = What is the concentration, in mol/L, of a solution formed by dissolving 28.0g of calcium chloride in enough water to make 225 mL of solution? Step 1: Find the number of moles of calcium chloride using n=m/M n= = m M = 0.252 mol CaCl2 28.0 110.98

Step 2: Use c=n/V to calculate the molar concentration c= = Notice the volume has been converted from mL to L 0.252 0.225 L = 1.12 mol/L

How many grams of sodium nitrate would be needed to make 425 mL of 6 How many grams of sodium nitrate would be needed to make 425 mL of 6.00 mol/L solution? Step 1: Find the number of moles using n= cV n= (6.00 mol/L)(0.425L) = 2.55 mol of sodium nitrate Step 2: Calculate how many grams is needed using m = nM m = (2.55 mol) (85.00 g/mol) = 217 g of NaNO3

What final solution volume would be required to prepare A 0.100 mol/L solution of AgNO3(aq) if 1.20 g of the solid salt will be used? MMAgNO3 = 169.9 g/mol C = 0.100 mol/L mAgNO3 = 1.20 g V = ? nAgNO3 = m/MM = 1.20 g 169.9g/mol = 0.00706 mol V = n/C = 0.00706 mol/0.100 mol/L = 0.0706 L

Mass/Volume Percent Mass of solute dissolved in a volume of solution, expressed as a % Mass/volume percent = x 100% Example: Saline solution contains 0.9g of sodium chloride dissolved in 100 mL of solution or 0.9% Mass of solute (in g) Volume of solution (in mL)

What is the percent (m/v) of the solution? A pharmacist adds 2.00 mL of distilled water to 4.00g of a powdered drug. The final volume of the solution is 3.00 mL. What is the percent (m/v) of the solution? Mass/volume percent= x 100% = x 100% mass of solute (in g) Volume of solution (in mL) 4.00 g 3.00 mL = 133%

b. What is the concentration of the drug in g/100 mL of solution? 133% means 133g/100 mL of solution Use ratios or cross out units to solve for the mass of solute in 100 mL x 100 mL 4.00 g 3.00 mL = x = X = 4.00g x 100ml x 1 3.00ml 4.00g x 100 mL 3.00 mL = 133 g = 133 g

Volume of solution (in mL) (m/v) percent = x 100% Many people use a solution of trisodium phosphate to clean walls before putting up wall paper. The recommended concentration is 1.7% (m/v). What mass of TSP is need to make 2.0 L solution? Mass of solute (g) Volume of solution (in mL) (m/v) percent = x 100% Rearrange the equation to solve for mass of solute Mass of solute= = (m/v) percent x volume of solution 100% 1.7% x 2000 mL 100% = 34 g

Concentration as a Volume/Volume Percent Volume/volume percent gives the volume of solute divided by the volume of solution Also referred to as percent (v/v), volume percent concentration Volume/volume percent = x 100% volume of solute (in mL) Volume of solution (in mL)

Volume/volume % x volume of solution 100% Rubbing alcohol is commonly used as an antiseptic for small cuts. It is sold as 70% (v/v) solution of isopropyl alcohol in water. What volume of isopropyl alcohol is used to make 500 mL of rubbing alcohol? Using this equation, Volume/volume percent = x 100 % Rearrange to solve for volume of solute: Volume of solute = = volume of solute Volume of solution Volume/volume % x volume of solution 100% 70% x 500 mL 100% = 350 mL 350 mL of isopropyl alcohol is used to make 500 mL of 70% (v/v) rubbing alcohol.

Concentration in parts per million or parts per billion ppm – parts per million (106)(one part solute per million parts of solution) ppb – parts per billion (109)(one part solute per billion parts of solution) Usually mass/mass relationships ie. The mass of solute compared with the mass of solution. ppm = x 106 OR mass of solute (g) Mass of solution (g) Mass of solute Mass of solution x g 106 g of solution =

A bottle of natural water contains 22 ppm of dissolved potassium ions A bottle of natural water contains 22 ppm of dissolved potassium ions. How many atoms of potassium are contained in a 500 mL bottle of the water? Assume the density of the solution is 1.000 g/mL)

The Maximum Acceptable Concentration (MAC) for lead in Canadian drinking water is 0.010 mg/L. What is this concentration expressed in parts per million? (Assume the density of the solution is 1.000 g/mL)

Mercury is a toxic compound Mercury is a toxic compound. Calculate the parts per billion (ppb) of mercury in a 100g water sample that contains 0.98mg of mercury.