Solutions and preparation
Look at the label on a bottle of concentrated acid in your chemistry lab. It never gives the molarity. It gives the percent purity by mass and the density. To know how much substance is really dissolved in each liter, you have to translate those factory figures into the language of the laboratory: moles per liter.
Molarity and other ways to express concentration
Dissolve 5 g of salt in one glass of water and 5 g of sugar in another. The masses are the same, but the numbers of particles are very different because the molar masses are different. How do we measure concentration so that we know how many particles will actually react in each liter?
A solution is a homogeneous mixture of a solute (the substance that dissolves) in a solvent (the substance it dissolves in, usually water). At a given temperature, a solution can be:
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unsaturated: it can still dissolve more solute;
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saturated: it holds the maximum amount of solute possible;
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supersaturated: it holds more than the saturation limit (unstable, and the extra solute can crystallize out suddenly).
Water is a good solvent for ionic and polar substances because its molecules are polar: the partially negative oxygen end attracts cations and the partially positive hydrogen ends attract anions, pulling the ions out of the crystal. A solute that makes ions in water (like NaCl) is an electrolyte and the solution conducts electricity. A solute that dissolves as whole molecules (like sugar) is a nonelectrolyte.
A standard solution is one whose concentration is known accurately.
Other units are used too, and you need to be able to convert between them. All of them describe the same thing: how much solute is in how much solution. (Mass percent is also called "percent by mass"; g/L is the "mass concentration".)
| Unit | Meaning | Typical use |
|---|---|---|
| g/L | mass of solute per liter of solution | lab work |
| mol/L (M) | moles of solute per liter of solution | chemical calculations |
| % m/m (mass percent) | g of solute per 100 g of solution | concentrated acids |
| % m/v | g of solute per 100 mL of solution | saline, medicines |
| % v/v | mL of solute per 100 mL of solution | rubbing alcohol, mixtures of liquids |
| ppm | mg of solute per liter (or per kg) of dilute aqueous solution | trace amounts, water quality |
In the laboratory, an aqueous solution is to be prepared by dissolving exactly $4.00\,\text{g}$ of pure sodium hydroxide, $\mathrm{NaOH}$, in deionized water to a total…
In the laboratory, an aqueous solution is to be prepared by dissolving exactly $4.00\,\text{g}$ of pure sodium hydroxide, $\mathrm{NaOH}$, in deionized water to a total volume of $250.0\,\text{mL}$ at $20\,^{\circ}\text{C}$. Atomic mass data: $M(\mathrm{Na}) = 22.99\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{O}) = 16.00\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{H}) = 1.01\,\text{g}\times\text{mol}^{-1}$.
- a) Calculate the molar concentration (molarity) of the resulting solution.
- b) State, with reasoning, which precision volumetric glassware must necessarily be used to set this final volume.
Percent purity and density of commercial reagents
Density is the bridge that lets you go from % m/m to g/L and then to mol/L. Use it only for that.
A commercial bottle of concentrated nitric acid, $\mathrm{HNO}3$, states on its label a purity of $65.0\,\%$ by mass and a density of…
A commercial bottle of concentrated nitric acid, $\mathrm{HNO}_3$, states on its label a purity of $65.0\,\%$ by mass and a density of $1.40\,\text{g}\times\text{cm}^{-3}$ at $20\,^{\circ}\text{C}$. Atomic mass data: $M(\mathrm{H}) = 1.01\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{N}) = 14.01\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{O}) = 16.00\,\text{g}\times\text{mol}^{-1}$.
- a) Calculate the mass of pure nitric acid present in $1.00\,\text{L}$ of this commercial reagent.
- b) Determine the molar concentration of this commercial solution.
$500.0\,\text{mL}$ of an aqueous solution of sulfuric acid, $\mathrm{H}2\mathrm{SO}4$, $0.250\,\text{mol}\times\text{L}^{-1}$ is to be prepared from a commercial acid of…
$500.0\,\text{mL}$ of an aqueous solution of sulfuric acid, $\mathrm{H}_2\mathrm{SO}_4$, $0.250\,\text{mol}\times\text{L}^{-1}$ is to be prepared from a commercial acid of $96.0\,\%$ purity by mass and density $1.84\,\text{g}\times\text{cm}^{-3}$. Atomic masses: $M(\mathrm{H}) = 1.01\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{S}) = 32.06\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{O}) = 16.00\,\text{g}\times\text{mol}^{-1}$.
- a) Calculate the volume of concentrated commercial acid that must be taken.
- b) Set out the experimental sequence for adding the reagents, justifying in detail the specific safety rule for avoiding serious thermal accidents.
Dilution: the moles stay the same
If you top off half a glass of very strong lemonade concentrate with water until the glass is full, the amount of concentrate has not changed but the taste is weaker. What exact relationship links the concentration to the total volume after you add solvent?
Serial dilutions
A serial dilution is a series of dilutions, each made from the one before. It is the quickest way to get a range of weak solutions, for example to make a calibration set. Dilution is also how you make a working solution from a stock solution.
A concentrated solution of hydrochloric acid, $\mathrm{HCl}$, with concentration $2.00\,\text{mol}\times\text{L}^{-1}$, is available in the lab. Exactly…
A concentrated solution of hydrochloric acid, $\mathrm{HCl}$, with concentration $2.00\,\text{mol}\times\text{L}^{-1}$, is available in the lab. Exactly $500.0\,\text{mL}$ of a dilute solution of $\mathrm{HCl}$ with concentration $0.050\,\text{mol}\times\text{L}^{-1}$ is required.
- a) Calculate the volume of concentrated solution that must be measured out to carry out this dilution.
- b) From the point of view of good lab practice and safety, explain which auxiliary instrument must necessarily be attached to the pipette to take the aliquot and which risky practice is strictly forbidden.
In the laboratory, a controlled dilution of a stock solution of copper(II) sulfate, $\mathrm{CuSO}4$, with initial concentration $0.800\,\text{mol}\times\text{L}^{-1}$,…
In the laboratory, a controlled dilution of a stock solution of copper(II) sulfate, $\mathrm{CuSO}_4$, with initial concentration $0.800\,\text{mol}\times\text{L}^{-1}$, is carried out. Using a volumetric pipette, an aliquot of $20.0\,\text{mL}$ is transferred to a volumetric flask of $250.0\,\text{mL}$, which is then made up with deionized water to $20\,^{\circ}\text{C}$. The equipment used and the detail of the final meniscus setting are illustrated below:
- a) Calculate the final molar concentration of the dilute solution obtained in the volumetric flask.
- b) A student adds water until the bottom of the meniscus is above the graduation mark when viewed at the level of the mark. Explain whether the real concentration will be higher or lower than the calculated one, and why removing some of that solution down to the mark does not correct its concentration.
Mixing solutions
When you mix two solutions of the same solute that do not react, the moles add up. If we assume the volumes are additive, the volumes add up too.
Evaporating water works the other way round: the moles of solute stay the same and the volume falls, so $M_1V_1 = M_2V_2$ still applies, with $V2 < V_1$.
When a problem gives you several sources of the same solute (solutions of different concentrations, or a solid of known purity), work out the moles from each source and add them up. Convert % m/m to moles using density and molar mass, and use the percent purity to find how much of a solid is really solute.
Two aqueous solutions of potassium chloride, $\mathrm{KCl}$, are mixed in the lab, with no chemical reaction taking place. Solution A has a volume of $150.0\,\text{mL}$…
Two aqueous solutions of potassium chloride, $\mathrm{KCl}$, are mixed in the lab, with no chemical reaction taking place. Solution A has a volume of $150.0\,\text{mL}$ and a concentration of $0.500\,\text{mol}\times\text{L}^{-1}$. Solution B has a volume of $350.0\,\text{mL}$ and a concentration of $1.200\,\text{mol}\times\text{L}^{-1}$. Assume ideal behavior with strictly additive volumes at $20\,^{\circ}\text{C}$.
- a) Calculate the final molar concentration of chloride ions, $\mathrm{Cl}^-$, in the resulting mixture.
- b) Calculate the volume of pure water that would have to be evaporated from the resulting mixture so that the final concentration of $\mathrm{KCl}$ reaches exactly $1.500\,\text{mol}\times\text{L}^{-1}$. In b), compare the volumes at $20\,^{\circ}\text{C}$ and assume that only water is lost, with no precipitation or change in the additivity of volumes.
Exactly $1.000\,\text{L}$ of an aqueous solution of sodium chloride, $\mathrm{NaCl}$, with a final concentration of $0.750\,\text{mol}\times\text{L}^{-1}$ at…
Exactly $1.000\,\text{L}$ of an aqueous solution of sodium chloride, $\mathrm{NaCl}$, with a final concentration of $0.750\,\text{mol}\times\text{L}^{-1}$ at $20\,^{\circ}\text{C}$ must be prepared. Three sources of the reagent are available in the lab: solution 1 ($200.0\,\text{mL}$ of $\mathrm{NaCl}$ $0.400\,\text{mol}\times\text{L}^{-1}$), solution 2 ($300.0\,\text{mL}$ of $\mathrm{NaCl}$ at $4.50\,\%$ by mass with density $1.03\,\text{g}\times\text{cm}^{-3}$) and a jar of $\mathrm{NaCl}$ solid anhydrous of $98.0\,\%$ purity by mass. Atomic masses: $M(\mathrm{Na}) = 22.99\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{Cl}) = 35.45\,\text{g}\times\text{mol}^{-1}$.
- a) Calculate the amount of substance (moles) of $\mathrm{NaCl}$ contributed jointly by solutions 1 and 2.
- b) Calculate the mass of impure solid reagent that must be weighed to make up the necessary moles, placing it in the $1.000\,\text{L}$ volumetric flask before finally making up to the mark with deionized water.
Preparing a standard solution in the laboratory
When you look at water in the narrow neck of a flask, the surface is not flat but curved. Where exactly on that curve should the mark sit if the concentration is not to be wrong? Lab glassware includes beakers, Erlenmeyer flasks, graduated cylinders, pipettes, burets and volumetric flasks, and only some of them are precise enough for a standard solution.
Primary standards
A primary standard is a substance used to make a standard solution directly from a weighed mass. To be suitable it must be:
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pure (known, very high purity);
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stable: it does not react with the air or absorb water or carbon dioxide, so its mass does not change while you weigh it;
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soluble in the solvent;
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of high molar mass, so that the mass you weigh is large and the weighing error is small in proportion.
Anhydrous sodium carbonate, $\mathrm{Na_2CO_3}$, and potassium hydrogen phthalate are primary standards. Sodium hydroxide is not: the pellets absorb water and carbon dioxide from the air, so the mass you weigh is not all NaOH. A NaOH solution therefore has to be standardized afterwards by titration against a primary standard.
Reading the volume
The method
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Weigh the solute on an electronic balance, into a clean weighing boat or directly into a beaker.
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Dissolve it in a beaker with a little deionized water, stirring with a glass rod.
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Transfer the solution to the volumetric flask through a funnel. Rinse the beaker, rod and funnel into the flask.
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Add water until it is just below the mark, then add the last drops with a dropper until the bottom of the meniscus touches the mark.
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Stopper and invert the flask several times to mix.
Precision and accuracy
Precision is how close repeated measurements are to each other. Accuracy is how close a measurement is to the true value. A volumetric flask and a volumetric pipette are precise to a small tolerance, and a graduated cylinder is not. Random errors (reading, small fluctuations) reduce precision. Systematic errors (a badly calibrated balance, always reading from above) reduce accuracy.
Safe practice
Before you start, read the SDS (safety data sheet) of each reagent: what is hazardous, how could you be harmed, and what will you do to prevent it. Wear safety goggles, a lab coat and gloves, and work in a fume hood with volatile or fuming reagents.
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Always use a pipette bulb or pipette filler. Never pipette by mouth.
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When diluting a concentrated acid, add the acid slowly to the water, stirring, never the reverse. Dilution is strongly exothermic. If you pour water onto the acid, the heat released can boil the water locally and throw drops of acid out of the container.
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For a strongly exothermic dilution, let the beaker cool before making up to the mark. A hot solution has a larger volume, and the concentration will be wrong when it cools.
A technician tries to prepare $500.0\,\text{mL}$ of standard solution of $\mathrm{NaOH}$ $0.1000\,\text{mol}\times\text{L}^{-1}$ by weighing $2.000\,\text{g}$ of…
A technician tries to prepare $500.0\,\text{mL}$ of standard solution of $\mathrm{NaOH}$ $0.1000\,\text{mol}\times\text{L}^{-1}$ by weighing $2.000\,\text{g}$ of commercial pellets and making up to the mark with deionized water in a volumetric flask. When this solution is subsequently titrated against potassium hydrogen phthalate (primary standard), the real molarity obtained is found to be only $0.0885\,\text{mol}\times\text{L}^{-1}$. Atomic masses: $M(\mathrm{Na}) = 22.99\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{O}) = 16.00\,\text{g}\times\text{mol}^{-1}$; $M(\mathrm{H}) = 1.01\,\text{g}\times\text{mol}^{-1}$.
- a) Assuming that the volume was made up exactly to $500.0\,\text{mL}$, and that the impurities present in this batch are water and substances that do not react in the titration, determine the real percentage purity in $\mathrm{NaOH}$ of the commercial pellets used.
- b) Explain, with reasoning, two chemical and experimental reasons why solid $\mathrm{NaOH}$ can never be considered a direct primary standard, and justify why it is necessary to carry out a standardization titration.
Back to the start: to know how much solute is in a bottle of reagent, take the label (percentage purity and density), work out the molarity with $c = 1000\,d\,(\%/100)/M$, and then measure the exact volume $V = n/c$ with a pipette before diluting in a volumetric flask. As a check on the ppm idea we met at the start, a water supply fluoridated at $0.7$ ppm contains only $0.7\ \text{mg}$ of fluoride per liter.