Exercises: Solutions and their properties

In the laboratory, $0.5\ \text{mol}$ of sodium chloride is dissolved in water to make $2\ \text{L}$ of solution.

1. a) Write down the formula for molarity.
2. b) Calculate the molarity of the solution.

To rehydrate an athlete, a drink is prepared by dissolving $20\ \text{g}$ of glucose in $180\ \text{g}$ of water.

1. a) What is the total mass of the solution?
2. b) Calculate its percentage by mass of glucose.

A solution of sodium hydroxide, $\text{NaOH}$, is $0.4\ \text{M}$. Data: molar mass of $\text{NaOH}$, $40\ \text{g/mol}$.

1. a) How many moles of $\text{NaOH}$ are in $250\ \text{mL}$ of that solution?
2. b) How many grams of $\text{NaOH}$ is this?

The legal limit of nitrates in drinking water is $50\ \text{ppm}$, i.e. $50\ \text{mg}$ of nitrate per kilogram of water.

1. a) How many milligrams of nitrate, at most, can a container with $5\ \text{kg}$ of water contain?
2. b) In the laboratory, $50\ \text{ppm}$ is often taken as $50\ \text{mg/L}$: explain what is being assumed about the density of water for both ways of expressing it to coincide.

Physiological saline used in hospitals is a $0.9\ \%$ by mass sodium chloride solution.

1. a) How many grams of salt are contained in a $500\ \text{g}$ bag of saline?
2. b) How many grams of water?

State whether each statement is true or false and justify your answer:

1. a) If half of a solution is transferred to another beaker, the molarity in each beaker is half of what it was at the beginning.
2. b) If the volume of a solution is halved by evaporating water, its molarity doubles.
3. c) Two solutions of different solutes can have the same molarity and, at the same time, different masses of solute per litre.

To prepare $100\ \text{mL}$ of a $0.5\ \text{M}$ sodium carbonate solution, $5.3\ \text{g}$ of solute must be weighed out. Put the following laboratory procedure steps in order (they are currently mixed up) and explain what is done in each step:

1. a) Make up to the mark on the neck of the flask with distilled water.
2. b) Weigh the solute using the balance.
3. c) Dissolve the solute in a beaker with a small amount of water.
4. d) Transfer to the $100\ \text{mL}$ volumetric flask and add water almost up to the mark.

In addition, explain what "making up to the mark" means and why the volumetric flask is the appropriate piece of equipment. The figure shows the volumetric flask and, magnified, the detail of making up to the mark on the neck.

Analysis of a spring finds $30\ \text{mg}$ of dissolved fluoride per $2\ \text{kg}$ of water. The recommended limit for drinking water is $1.5\ \text{ppm}$.

1. a) Express the fluoride concentration of the spring in ppm.
2. b) Does it exceed the limit? How many times does it exceed it?

$20\ \text{g}$ of sodium hydroxide, $\text{NaOH}$, are dissolved in water to make up $500\ \text{mL}$ of solution. Given: molar mass of $\text{NaOH}$, $40\ \text{g/mol}$.

1. a) How many moles are the $20\ \text{g}$ of $\text{NaOH}$?
2. b) Express the volume in litres and calculate the molarity of the solution.

You are asked to prepare $200\ \text{mL}$ of a $1\ \text{M}$ solution of potassium chloride, $\text{KCl}$. Given: molar mass of $\text{KCl}$, $74.5\ \text{g/mol}$.

1. a) How many moles of $\text{KCl}$ do you need?
2. b) What mass should you weigh?
3. c) Describe the complete laboratory procedure, naming the apparatus (balance, beaker, volumetric flask…) and the moment when it is made up to the mark.

$10\ \text{mL}$ of a hydrochloric acid solution, $\text{HCl}$, $2\ \text{M}$ are taken and water is added to make up $100\ \text{mL}$ of solution. Observe the diagram of the dilution.

1. a) How many moles of $\text{HCl}$ did the initial $10\ \text{mL}$ contain?
2. b) Calculate the molarity of the diluted solution.
3. c) Verify that the relationship $M_1\times V_1=M_2\times V_2$ is satisfied and explain which quantity is conserved in a dilution.

A pharmacy dilutes $50\ \text{g}$ of a concentrated salt solution at $20\ \%$ by mass with $150\ \text{g}$ of water to prepare mouthwashes.

1. a) How many grams of salt are provided by the concentrated solution?
2. b) What is the total mass of the mixture?
3. c) Calculate the new percentage by mass.

A patient needs to receive $0.05\ \text{mol}$ of glucose intravenously and a $0.5\ \text{M}$ glucose solution is available. Given: molar mass of glucose, $180\ \text{g/mol}$.

1. a) What volume of solution, in litres, contains that amount of glucose? Express it in millilitres as well.
2. b) How many grams of glucose does the patient receive?

A laboratory has nitric acid, $\text{HNO}_3$, $4\ \text{M}$ and needs to prepare $500\ \text{mL}$ of $0.8\ \text{M}$ solution.

1. a) Apply the relationship $M_1\times V_1=M_2\times V_2$ to calculate the volume of concentrated acid that needs to be measured.
2. b) Describe how to safely prepare the dilution: what apparatus is used and why the acid is added to the water and not the other way round.

The colligative properties of solutions depend on the number of dissolved solute particles and not on their nature.

1. a) Order from lowest to highest freezing point: pure water, $0.5\ \text{M}$ salt solution, and $1\ \text{M}$ salt solution. Explain your answer.
2. b) Order those same three samples from lowest to highest boiling point.
3. c) Does it affect these orderings whether the solute is salt or sugar? Explain what it means for them to be colligative properties.

A glucose solution has a density of $1.08\ \text{g/mL}$ and a concentration of $5\ \%$ by mass. Given: molar mass of glucose, $180\ \text{g/mol}$.

1. a) Calculate the mass of $1\ \text{L}$ of solution.
2. b) How many grams of glucose does that litre contain?
3. c) Calculate the molarity of the solution.

Commercial hydrochloric acid used in the laboratory has a concentration of $37\ \%$ by mass and a density of $1.19\ \text{g/mL}$. Given: molar mass of $\text{HCl}$, $36.5\ \text{g/mol}$.

1. a) Calculate the mass of $1\ \text{L}$ of commercial acid.
2. b) How many grams of pure $\text{HCl}$ does that litre contain?
3. c) Calculate the molarity of the commercial acid, to one decimal place.
4. d) Calculate, to one decimal place, what volume of this acid must be measured to prepare $500\ \text{mL}$ of $1\ \text{M}$ solution, and describe the dilution procedure safely.

In an analytical laboratory, $100\ \text{mL}$ of $0.5\ \text{M}$ $\text{NaCl}$ solution are mixed with $300\ \text{mL}$ of $1.5\ \text{M}$ $\text{NaCl}$ solution. Assume that the volumes are additive. The diagram shows the mixture.

1. a) Calculate the moles of salt provided by each solution.
2. b) Calculate the molarity of the resulting mixture.
3. c) Explain why the result is not $1\ \text{M}$, the mean of the two initial concentrations.

A pot contains $2\ \text{kg}$ of broth with $1\ \%$ by mass of salt.

1. a) How many grams of salt are in the broth?
2. b) Upon boiling, water evaporates until the broth weighs $500\ \text{g}$: what is the percentage by mass of salt now?
3. c) A chef wants the broth to have $2\ \%$ salt: to what total mass must it be reduced?
4. d) Explain why the concentration increases even though not a single gram of salt has been added: which quantity is conserved?

In winter, road services spread salt on ice and snow.

1. a) What happens to the freezing point of water when a salt is dissolved?
2. b) Explain why the mixture of water and salt can remain liquid at $-5\ \celsius$ even though pure water would be frozen.
3. c) Reason why this method loses effectiveness when it is very cold, for example at $-20\ \celsius$: what do you think happens when the temperature drops too low, no matter how much salt is added?
4. d) Relate this method to car antifreeze: which colligative property do both make use of?

Two compartments are separated by a semipermeable membrane, which allows water to pass through but not glucose. In one there is a $0.1\ \text{M}$ glucose solution and in the other a $1\ \text{M}$ solution. The diagram shows the initial situation.

1. a) Explain what osmosis is.
2. b) Predict which way the water will pass through the membrane and justify your answer.
3. c) What difference will be observed between the two compartments over time?
4. d) What is osmotic pressure? State what would need to be done to prevent this flow of water.

A desalination plant obtains drinking water from the sea by reverse osmosis. The diagram shows the process.

1. a) Explain what reverse osmosis consists of and what is achieved by applying a pressure higher than its osmotic pressure to seawater.
2. b) What characteristic must the membrane have for the process to work?
3. c) Brackish water, less concentrated in salts than seawater, requires less pressure to desalinate: relate this to the dependence of osmotic pressure on concentration.
4. d) Point out an advantage and a disadvantage of the process considering the energy required.

Red blood cells are surrounded by a semipermeable membrane and contain an aqueous medium with dissolved salts and proteins.

1. a) Explain why saline or intravenous fluid injected into a vein must be isotonic, that is, have a solute concentration similar to that of blood. Which colligative phenomenon is involved?
2. b) Predict what would happen to red blood cells if the IV fluid were much more dilute than blood: which way would water flow and what risk would there be?
3. c) What if it were much more concentrated? Justify your answer in the same way.

Car antifreeze is a solution of ethylene glycol in water.

1. a) Which colligative property does it make use of to protect the engine in winter? Explain how it works at $-15\ \celsius$.
2. b) The same solution also raises the boiling point of the coolant water: explain why this is useful in summer.
3. c) A garage prepares the mixture at $30\ \%$ by mass of ethylene glycol: calculate how many kilograms of ethylene glycol and water are needed to obtain $10\ \text{kg}$ of antifreeze.
4. d) If the cooling system of a car contains $6\ \text{kg}$ of that mixture, what mass of ethylene glycol does it contain?

Unit challenge. How much gas does a soft drink contain and how does it affect the properties of the solution? Determine the concentration of dissolved $CO_2$ and its ideal gas behavior right in your own kitchen.

1. Local conditions: Look up the atmospheric pressure ($P \pm 1\text{ hPa}$) and ambient temperature ($T \pm 0.5\text{ }^\circ\text{C}$) in your town or city on the Met Éireann website.

2. Home experimentation: Weigh a small bottle of sparkling water using a kitchen scale (sensitivity $\pm 0.1\text{ g}$). Degas it progressively by shaking it and opening it carefully over $4$ successive intervals, recording the mass of the system after each gas loss. Finally, degas it completely (shaking until the mass no longer changes) to obtain the final mass $m_f$, and note the liquid volume $V_{\text{dis}}$ shown on the label.

3. Processing and calculation: Prepare a table showing the mass of $CO_2$ lost and propagate its uncertainty. Using the ideal gas equation ($PV = nRT$), deduce the volume of gas released and calculate the molar concentration of the gas that remained dissolved at each stage.

4. Final report: Plot the graph of gas volume versus mass lost (including error bars) and explain how pressure and temperature affect the solubility of the gas.

Evaluation criteria:

• Rigorous determination of home measurements with their associated uncertainties.

• Correct application of the ideal gas law and concentration units.

• Analytical quality of the table, graph, and physicochemical interpretation of the results.