In the previous few posts, we introduced the different ways of expressing the concentration of a solution and how each one is used in chemical calculations. These include molarity (M), molality (m), percent compositions, and other related units, all of which describe how much solute is present relative to a given amount of solution or solvent.
Before starting the practice problems, let’s briefly review the two most commonly used concentration units:
- Molarity (M) is defined as the number of moles of solute per liter of solution. In other words, it tells you how many moles of a substance are present in a given volume of the entire mixture (solute + solvent). It is expressed in units of mol/L.
- Percent concentration is defined as the amount of solute relative to the total amount of solution, expressed as a percentage. Depending on how the quantities are measured, it is most often given as percent by mass (mass of solute per mass of solution × 100%), percent by volume (volume of solute per volume of solution × 100%), or mass/volume percent (grams of solute per 100 mL of solution).
- Molality (m) is defined as the number of moles of solute per kilogram of solvent. Unlike molarity, it depends only on mass rather than volume, and is expressed in units of mol/kg.
With these definitions in mind, you can now apply them to solve a variety of concentration problems.
1.
Identify the solvent and solute(s) in a sample of an antiseptic that contains 65% propanol, 20% ethanol, and 15% water.
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2.
What is the molarity of the solution prepared by dissolving 33.5 g sodium oxalate (Na2C2O4) in 250.0 ml water?
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3.
How many grams of silver nitrate (AgNO3) can be obtained from an 800.0 g sample of a 65% solution?
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4.
Commercial concentrated hydrochloric acid is 36.0% by mass with a density of 1.2 g/mL. Calculate the molarity of this solution.
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5.
A student has 2.0 L of 7.0 M hydrochloric acid, HCl. She wants to prepare a 1.5 M solution. How many liters of solution can she make?
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6.
What is the concentration of the solution made by mixing 100. mL of 2.0 M and 250. mL 3.5 M solutions of potassium iodide?
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7.
How many grams of copper(II) sulfate pentahydrate (CuSO4·5H2O) is needed to prepare 500. mL solution of 0.480 M CuSO4(aq)?
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8.
An ICU nurse is preparing for an intravenous administration of glucose (C6H12O6). How many mL of this solution will be needed to provide 6.50 mmol of glucose if the solution is labeled as 0.350 M?
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9.
How many milliliters of 0.850 M BaCl2 solution are needed to obtain 9.37 g of the salt?
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10.
Calculate the concentration of each ion and their total concentration in a solution prepared by dissolving 0.2500 mol of Ca(NO3)2 in 150.0 mL of water.
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11.
Calculate the molality of a 0.500 M solution (d = 1.09 g/mL) of baking soda (NaHCO3).
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12.
A solution contains 3.5 ×10–3 g of vitamin C in 1,625 mL of solution. What is the concentration of vitamin C in parts per million (ppm) if the density of the solution is 1.08 g/mL.
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13.
Calculate the mass percent, mole fraction, molality, and molarity of hexane (C6H14, d =0.660 g/cm3) when it is mixed with heptane (C7H12, d=0.684 g/cm3) in a 35.0 : 55.0 mL ratio. Assume that the volumes are additive.
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14.
Ethylene glycol (C2H6O2) is used in automobile antifreeze as a 40.0 mass % aqueous solution. Calculate the molarity, molality, and mole fraction of the ethylene glycol if the density of the solution is 1.05 g/cm3.
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15.
A solution containing 186.5 g of KCl in 813.5 g of water has a density of 1.106 g/mL. What is the molarity of the solution?
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16.
A lab specialist has 20% and 60% stock solutions of sodium hydroxide. Suppose she is asked to prepare 100 g of 35% solution. How many grams of each solution will she need to mix?
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17.
What is the molality of the solution prepared by mixing 625.2 grams of menthol (C10H20O) and 3,500. grams of ethanol (C2H5OH).
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18.
Calculate the molality of 31.0% MgCl2 solution with a density of 1.27 g/mL.
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19.
How many grams of barium chloride (BaCl2) are in a 0.025 molal solution if 3.50 kg of solvent was used to prepare it?
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20.
Determine the percentage concentration of 5.00 M HCl solution if its density is 1.104 g/mL.
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21.
Glycerol (CH3CH(OH)CH2OH) is widely used in FDA-approved wound and burn treatments. What volume of glycerol (d = 1.26 g/mL), must be added to one kilogram of water to produce a solution with 5.00 mass % glycerol?
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22.
A bottle of rum contains 40% ethanol by volume. The density of ethanol (C2H5OH) is 0.789 g/cm3. Calculate the mass percent and molality of ethanol in the rum.
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23.
15.00 mL of propanol (CH3CH2CH2OH) was dissolved in sufficient volume of water to prepare 100.0 mL of a solution with a density of 0.983 g/mL. Given the density of propanol is 0.803 g/mL, determine its concentration expressed as (a) volume percent; (b) mass percent; (c) mass/volume percent; (d) mole fraction; (e) mole percent; (f) molarity; (g) molality?
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