Exercises: Solutions and their properties

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

1. a) Write 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?

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 liter.

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.

$20\ \text{g}$ 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 liters 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 liters, contains that amount of glucose? Express it in milliliters 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 around.

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 liter contain?
3. c) Calculate the molarity of the solution.

Commercial hydrochloric acid used in the lab 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 liter 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?

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 city on the National Weather Service 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 data 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 data table, graph, and physicochemical interpretation of the results.