The Concentration of Solutions

Phenol is a hazardous liquid, especially when it is at room temperature. It is a volatile chemical. Inhaling phenol affects the central nervous system and can lead to a coma. Coma and death have been known to occur within ten minutes after phenol has contacted the skin. One gram of phenol can be fatal if swallowed.

Would you expect to find such a hazardous chemical in over the counter medications? Phenol is listed as an ingredient in many throat sprays and lotions to relieve itching. You may also find it in antiseptic or disinfectant. Whether phenol is hazardous, or beneficial, depends entirely on concentration. At a low concentration, phenol is a safe component of certain medicines.

Concentration is the amount of solute per quantity of solvent. In this section, you will earn about various ways that chemists use to express the concentration of a solution. You will also find the concentration of a solution by experiment.

Concentration as a Mass/Volume Percent Recall that the solubility of a compound at certain temperatures is often expressed as the mass of the solute per 100 mL of solvent. 36 g/ 100 mL sodium chloride solution has 36 g of sodium chloride in 100 mL of water at room temperature. The final volume of sodium chloride solution may not be 100 mL. It is the volume of solvent that is important.

Chemists often express the concentration of an unsaturated solution as the mass of the solute dissolved per volume of solution. This is different from solubility. It is usually expressed as a percent relationship. A mass/volume percent gives the mass of solute dissolved in a volume of solution, expressed as a percent. Mass/volume percent is also referred to as the percent (m/v).

Percent (m/v)= mass of solute (g)X 100% volume of solution (mL)

Suppose that a hospital patient requires an intravenous drip to replace lost fluids. The intravenous fluid may be saline solution that contains 0.9 g of sodium chloride dissolved in 100 mL of solution. 0.9 g/100 mL x 100% = 0.9% (m/v)

Solving for Mass/Volume Percent Example A pharmacist adds 2.00 mL of distilled water to 4.00 g of powdered drug. The final volume of solution is 3.00 mL. What is the concentration of the drug in g/100 mL of solution? And what is the percent (m/v) of the solution?

Two Ways to Solve the Problem Method 1 % (m/v) = mass of solute x 100% volume of solution % (m/v) = 4.00 g x 100% 3.00 mL % (m/v) = 133% this means 133 g per 100 mL Method 2 x = 4.00 g 100 mL 3.00mL x = 1.33 g/mL 100 mL x =133 g this means 133 g per 100 mL or 133%

Finding Mass for an (m/v) Concentration Example Many people use a solution of trisodium phosphate (Na 3 PO 4 ) to clean walls before putting up wallpaper. The recommended concentration is 1.7% (m/v). What mass of TSP is needed to make 2.0 L of solution?

Method 1 %(m/v) = mass of solute x 100% volume of solution mass of solute = volume x %(m/v) 100% mass = (2000 mL)(1.7%) 100% mass = 34 g Method g=x 100 mL 2000 mL 100 x = 3400 x = 34 g 34 g of TSP is needed for 2.0 L of solution

Concentration as a Mass/Mass Percent The concentration of a solution that contains a solid solute dissolved in a liquid solvent can also be expressed as a mass of solute dissolved in a mass of solution. This is usually expressed as a percent relationship. A mass/mass percent gives the mass of solute divided by the mass of solution, expressed as a percent. The mass/mass percent is also referred to as percent (m/m).

Percent (m/m) = mass of solute (g)x 100% mass of solution (g)

A 100 g of seawater contains g of magnesium ion (along with other substances) g/100 g x 100% = 0.129% Mg 2+

Composition of Some Alloys AlloyUsesTypical (m/m) percent BrassMusical instruments, ornaments Cu (85%), Zn (15%) BronzeStatues, castingsCu(80%), Zn(10%), Sn(10%) Cupronickel“Silver” coinsCu (75%), Zn (25%) Dental amalgamDental fillingsHg(50%), Ag(35%), Sn(15%) DuraluminAircraft partsAl (93%), Cu (5%), other (2%) PewterOrnamentsSn (85%), Cu (7%), Bi (6%), Sb (2%) Stainless SteelCutleryFe (78%), Cr (15%), Ni (7%) Sterling SilverJewellryAg (92.5%), Cu (7.5%)

Solving for Mass/Mass Percent Example 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 nearby road, a student took a sample of slush to analyze it. The sample had a mass of g. When the solution evaporated, the residue had a mass of 4.58 g. Assume no other solutes were present. What was the mass/mass percent of the CaCl 2 in the slush? And how many grams were present in 100 g of solution?

Method 1 %(m/m) = mass of solute x 100% mass of solution %(m/m) = 4.58 g x 100% g %(m/m) = 19.51% 19.5 g of solute per 100 g of solution Method 2 x =4.58 g 100 g23.47 g x = 458 x = 19.5 g

Concentration as a Volume/Volume Percent When mixing two liquids to form a solution, it is easier to measure their volumes than their masses. A volume/volume percent gives the volume of solute divided by the volume of solution, expressed as a percent. The volume/volume percent is also referred to as percent (v/v) or percent by volume.

Percent (v/v)= volume of solute (mL)X 100% volume of solution (mL)

Solving for a Volume/Volume Percent Rubbing alcohol is commonly used as an antiseptic for small cuts. It is sold as a 70% (v/v) solution of isopropyl alcohol in water. What volume of isopropyl alcohol is used to make 500 mL of rubbing alcohol?

Method 1 %(v/v) = vol of solute x 100% vol of solution Vol of solute = (%)(vol of soln) 100% vol of solute = (70%)(500 mL) 100% vol of solute = 350 mL Method 2 x =70 mL 500 mL100 mL 100 x = 3500 x = 350 mL It takes 350 mL of isopropyl alcohol to make 500 mL of 70% (v/v)

Concentration in Parts per Million and Parts per Billion The concentration of a very small quantity of a substance in the human body, or in the environment, can be expressed in ppm or ppb. ppm and ppb are usually mass/mass relationships and they describe the amount of solute that is present in a solution. ppm and ppb do not refer to the number of particles, but the mass of a solute compared to the mass of a solution.

ppm = mass of solute x 10 6 mass of solution OR mass of solute= x mass of solution 10 6 g of soln ppb = mass of solute x 10 9 mass of solution OR mass of solute= x mass of solution 10 9 g of soln

PPB in Peanut Butter! A fungus that grows on peanuts produces a deadly toxin. When ingested in large amounts, this toxin can destroy the liver and cause cancer. Any shipment of peanuts that contains more than 25 ppb of this dangerous fungus is rejected. A company receives 20 tonne (20 x 10 6 g) of peanuts to make peanut butter. What is the maximum mass of fungus that is allowed?

Method 1 ppb = mass of fungus x 10 9 mass of peanuts fungus = (ppb)(peanuts) 10 9 fungus = (25)(20 x 10 6 ) 10 9 fungus = 0.5 g Method 2 mass of solute= x mass of solution 10 9 g of soln ?= 25 g 20 x g of soln ? = 0.5 g