Solutions
A can of fizzy drink contains dissolved sugar, but it also has a label with numbers: "10,6 g of sugar per 100 mL". In 2nd ESO you learnt how to talk about solutions. Now it is time to work with them using real numbers, the same ones a laboratory uses or those on the label of any product in the supermarket.
Revision: concentration as a percentage by mass
If you dissolve a spoonful of cocoa in half a glass of milk and an identical spoonful in a full mug, the first glass ends up darker and sweeter even though both contain the same amount of cocoa: how do we measure that proportion numerically by comparing masses?
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…
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, Marcos dissolves $5\ \text{g}$ of salt in $95\ \text{g}$ of water. a) How many grams of solution does he obtain in total? b) Percentage by mass is calculated…
To gargle, Marcos dissolves $5\ \text{g}$ of salt in $95\ \text{g}$ of water.
- a) How many grams of solution does he obtain in total?
- 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?
Concentration in grams per litre
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…
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?
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:…
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.
Converting from one concentration to another using density
To convert between percentage by mass and g/L you need the density of the solution: the bridge between mass and volume.
You are asked to prepare $500\ \text{mL}$ of a copper sulphate solution with a concentration of $8\ \text{g/L}$. a) How many grams of copper sulphate should you weigh…
You are asked to prepare $500\ \text{mL}$ of a copper sulphate solution with a concentration of $8\ \text{g/L}$.
- a) How many grams of copper sulphate should you weigh out?
- 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?
A surface disinfectant label states "$70\ \%$ alcohol by volume". How many millilitres of alcohol does a $250\ \text{mL}$ bottle of this disinfectant contain?
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…
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 $12\ \text{g/L}$.
- a) What volume of the stock solution must you measure?
- 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.
- 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 $500\ \text{mL}$?
Solubility, saturation and mixing solutions
If you put a teaspoon of salt into a glass of water it dissolves straight away, but if you keep adding spoonfuls there comes a point when the grains pile up at the bottom no matter what you do: what is the exact limit of solute that a solvent can take?
To clean silver, Julia prepares a solution with $40\ \text{g}$ of sodium hydrogen carbonate in $360\ \text{g}$ of water. a) What total mass of solution does she obtain?…
To clean silver, Julia prepares a solution with $40\ \text{g}$ of sodium hydrogen carbonate in $360\ \text{g}$ of water.
- a) What total mass of solution does she obtain?
- b) Calculate its percentage by mass of bicarbonate.
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…
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.
- a) How many grams of salt does each solution provide?
- b) What is the concentration of the mixture, in $\text{g/L}$?
- 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. a) How many grams of potassium nitrate and how many…
For a crystallisation experiment, you must prepare $400\ \text{g}$ of a $8\ \%$ by mass potassium nitrate solution.
- a) How many grams of potassium nitrate and how many grams of water should you weigh?
- 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.
- c) Then you add $100\ \text{g}$ more of water. What is the new percentage by mass?
Back to the start: the $10{,}6\ \text{g}$ per $100\ \text{mL}$ of the fizzy drink are equivalent to a concentration of $106\ \text{g/L}$; a standard $330\ \text{mL}$ can therefore contains about $35\ \text{g}$ of sugar, which is almost nine sugar cubes.