Exercises: Solutions

To fertilise her balcony plants, Nora dissolves $30\ \text{g}$ of soluble fertilizer in water to make $2\ \text{L}$ of solution. Mass concentration is calculated by dividing the grams of solute by the litres of solution. What is the concentration of the fertilizer, in $\text{g/L}$?

To gargle, Cian dissolves $5\ \text{g}$ of salt in $95\ \text{g}$ of water.

1. a) How many grams of solution does he obtain in total?
2. b) Percentage by mass is calculated by dividing the mass of solute by the total mass of solution and multiplying by $100$. What is the percentage by mass of salt?

A homemade hand sanitiser gel is prepared by mixing $30\ \text{mL}$ of alcohol with aloe vera to make up $150\ \text{mL}$ of gel. Percentage by volume is calculated by dividing the volume of solute by the total volume of solution and multiplying by $100$. What is the percentage by volume of alcohol in the gel?

Dry air is a solution of gases: $78\ \%$ of nitrogen, $21\ \%$ of oxygen and $1\ \%$ of argon and other gases, by volume. The figure summarizes this composition.

1. a) What is the solvent in air? Give reasons for your answer.
2. b) Approximately how many litres of oxygen are there in $10\ \text{L}$ of air?

In the laboratory, you are going to prepare $250\ \text{mL}$ of a solution using a volumetric flask. Put these steps in order and explain each one in your own words:

1. a) Top up with water to the mark on the neck of the flask.
2. b) Weigh the solute on the balance.
3. c) Dissolve the solute in a beaker with a little water.
4. d) Transfer the solution to the flask using a funnel and add water almost up to the mark.

What exactly does "topping up to the mark" mean?

Diluted bleach for mopping the floor contains $5\ \text{g}$ of sodium hypochlorite per litre. If you fill a bucket with $4\ \text{L}$ of this solution, how many grams of hypochlorite are in the bucket?

A hospital glucose drip bag has a concentration of $5\ \%$ by mass of glucose.

1. a) How many grams of glucose does a $500\ \text{g}$ bag of glucose solution contain?
2. b) And how many grams of water?

Complete the sentence with the missing words: "Concentration in grams per litre relates the mass of $\dots$ to the $\dots$ of solution; percentage by mass relates the mass of solute to the total $\dots$ of solution; and percentage by $\dots$ is used mainly when the solute is a liquid or a gas." Then give an example of a solution for each of the three ways of expressing concentration.

In the laboratory, Aitana dissolves $12\ \text{g}$ of potassium nitrate in water to make $300\ \text{mL}$ of solution. Calculate the concentration in $\text{g/L}$. Note: convert the volume to litres first.

You are asked to prepare $500\ \text{mL}$ of a copper sulphate solution with a concentration of $8\ \text{g/L}$.

1. a) How many grams of copper sulphate should you weigh out?
2. b) Describe how you would prepare the solution in the laboratory, naming the apparatus you would use (balance, beaker, funnel, $500\ \text{mL}$ volumetric flask...) and at what point you top up to the mark.

A surface disinfectant label states "$70\ \%$ alcohol by volume". How many millilitres of alcohol does a $250\ \text{mL}$ bottle of this disinfectant contain?

To clean silver, Julia prepares a solution with $40\ \text{g}$ of sodium hydrogen carbonate in $360\ \text{g}$ of water.

1. a) What total mass of solution does she obtain?
2. b) Calculate its percentage by mass of bicarbonate.

The label on a carton of milk states that it provides $125\ \text{mg}$ of calcium per $100\ \text{mL}$ of milk.

1. a) Express this concentration in $\text{g/L}$.
2. b) How many milligrams of calcium do you consume if you have a $200\ \text{mL}$ glass of milk for breakfast?

For mopping, you dilute $50\ \text{mL}$ of bleach at $40\ \text{g/L}$ in water to make $2\ \text{L}$ of solution. Look at the diagram of the dilution.

1. a) How many grams of hypochlorite are in those $50\ \text{mL}$ of bleach?
2. b) What is the concentration of the solution in the bucket, in $\text{g/L}$?
3. c) Explain why the mass of hypochlorite does not change when adding water, even though the concentration does.

An aquarium needs a treatment of $10\ \text{g}$ of a medication sold as a $25\ \text{g/L}$ solution.

1. a) What volume of solution must you measure, in litres?
2. b) Express it in millilitres.

You have $50\ \text{mL}$ of a dye solution at $36\ \text{g/L}$ and you want to obtain a solution of $12\ \text{g/L}$.

1. a) To what final volume must you dilute it with water?
2. b) Approximately what volume of water needs to be added?
3. c) Check the result using $c_1\times V_1=c_2\times V_2$.

A laboratory purchases a stock solution of a reagent with a concentration of $60\ \text{g/L}$. For a lab practical, you need $500\ \text{mL}$ of a diluted solution of $12\ \text{g/L}$.

1. a) What volume of the stock solution must you measure?
2. b) Describe the entire procedure in the laboratory: what equipment you use (pipette or graduated cylinder, $500\ \text{mL}$ volumetric flask, dropper…) and what bringing to the mark means.
3. c) Why is it not enough to just measure the calculated volume of stock solution and add the rest of the water measured with a graduated cylinder to reach $500\ \text{mL}$?

You mix $200\ \text{mL}$ of a $30\ \text{g/L}$ salt solution with $300\ \text{mL}$ of another salt solution at $10\ \text{g/L}$ in the same container. Assume the final volume is the sum of the two. The diagram shows the mixture.

1. a) How many grams of salt does each solution provide?
2. b) What is the concentration of the mixture, in $\text{g/L}$?
3. c) Why is the final concentration not $20\ \text{g/L}$, the mean of the two concentrations?

For a crystallisation experiment, you must prepare $400\ \text{g}$ of a $8\ \%$ by mass potassium nitrate solution.

1. a) How many grams of potassium nitrate and how many grams of water should you weigh?
2. b) Describe how you would prepare the solution and explain why this time you do not need a volumetric flask or to top up to the mark.
3. c) Then you add $100\ \text{g}$ more of water. What is the new percentage by mass?

A juice factory concentrates $800\ \text{kg}$ of juice containing $12\ \%$ by mass of sugars. Evaporating some of the water leaves $300\ \text{kg}$ of concentrated juice.

1. a) How many kilograms of sugars were there at the start?
2. b) How many kilograms of water evaporated?
3. c) What is the percentage by mass of sugars in the concentrated juice?
4. d) Explain why the percentage increased even though not a single gram of sugar was added.

The E5 petrol that Sara puts in her motorbike contains $5\ \%$ by volume of bioethanol.

1. a) How many litres of bioethanol are in a $20\ \text{L}$ tank of E5?
2. b) Sara mixes those $20\ \text{L}$ of E5 with $20\ \text{L}$ of ethanol-free petrol from a jerrycan. What percentage by volume of ethanol does the mixture have now?
3. c) Explain why it is incorrect to either add the percentages ($5\ \%+0\ \%=5\ \%$) or keep $5\ \%$.

You prepare solution A by dissolving $18\ \text{g}$ of salt in water to make $300\ \text{mL}$. Then you take $100\ \text{mL}$ of A, pour them into a flask and top up with water to $400\ \text{mL}$: this is solution B.

1. a) Calculate the concentration of A, in $\text{g/L}$.
2. b) How many grams of salt are in the $100\ \text{mL}$ taken from A?
3. c) Calculate the concentration of B from those grams.
4. d) Check that you get the same result using the dilution formula, $c_1\times V_1=c_2\times V_2$, and explain why it works: what is always conserved when diluting?

Three classmates each prepare $250\ \text{mL}$ of a $10\ \text{g/L}$ solution by weighing $2.5\ \text{g}$ of salt, but each makes a mistake:

1. a) Aoife does not tare the balance with the watch glass, so she actually weighs out less salt than she thinks.
2. b) Cian tops up the flask above the mark on the neck.
3. c) Niamh transfers the solution to the flask but forgets to rinse the remaining salt stuck to the beaker with a little water.

For each case, explain what the error consists of and reason whether the actual concentration of their solution is above, below or equal to $10\ \text{g/L}$.

A salt solution has a density of $1.05\ \text{g/mL}$ and a concentration of $10\ \%$ by mass.

1. a) What is the mass of $1\ \text{L}$ of this solution?
2. b) How many grams of salt are in that litre?
3. c) Express the concentration in $\text{g/L}$.
4. d) Is a $10\ \%$ solution by mass the same as a $10\ \text{g/L}$ solution? Give reasons for your answer using the previous results.