Standard solutions: mass, transfer and final volume
Key idea: Prepare a standard solution by weighing a suitable solute, dissolving it, transferring it quantitatively and making up to a known final volume. Mix thoroughly, then calculate concentration from n/V.
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Guided lesson
Guided steps
- Decide whether measuring water fixes the solution volume.
- Connect purity and composition to a known solute amount.
- Follow quantitative transfer, cooling, making up and mixing.
- Follow the mass-to-amount-to-concentration calculation.
- Calculate the transferred mass, concentration and overfilling effect.
- Find the concentration after removing some mixed solution.
- Explain why withdrawing solution does not undo overfilling.
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ContinueA titration can only give a trustworthy amount if the concentration of the reference solution is known. Preparing a standard solution connects an accurately measured solute amount to a known final solution volume.
Recall solution concentration and dilution: c = n/V, with V in dm³ when c is in mol dm⁻³.
Check your understanding 1 Water volume or solution volume?
A recipe needs 250.0 cm³ of sodium carbonate solution. A student adds 250.0 cm³ of water to the solid. Is the required final volume known?
Show answer
The required volume is the final solution volume after dissolving, at the flask mark. Dissolving a solute can change volume; 250.0 cm³ of water is not the same instruction.
What makes a suitable standard?
A standard solution has a known concentration. A primary standard is a substance that can be used to calculate that concentration directly from a measured mass and its molar mass. It must have sufficiently high purity, a known composition and stability during preparation and storage. Absorbing water or changing composition would break the link between weighed mass and solute amount.
A supplied, suitably dried sample of anhydrous sodium carbonate can be used as a primary standard. Its formula is Na₂CO₃; a hydrated sample would have a different molar mass. Follow the preparation method specified for the actual solid.
Keep the measured solute and fix the final volume
- Measure the mass actually transferred. For weighing by difference, record the container mass before and after transfer; subtract the second reading from the first.
- Dissolve the solid completely in deionised water in a beaker.
- Transfer into a volumetric flask through a funnel. Rinse the beaker, stirring rod and funnel into the flask. This quantitative transfer carries the measured solute into its final container.
- If dissolving warmed the solution, let it return to the flask’s calibration temperature before making up to the mark. Add water to just below the mark, then use a dropping pipette for the final adjustment. For this clear solution, align the bottom of the meniscus with the mark at eye level.
- Stopper and invert several times to mix thoroughly. The concentration calculation assumes a uniform solution.
A 250.0 cm³ flask specifies the volume of the whole solution at its calibration mark. Adding 250.0 cm³ of water to the solute is a different operation and does not set the required final solution volume.
Solute left in the beaker gives too little solute in the final volume. Overfilling gives too large a volume for the measured amount. Both lower concentration. Adding more water cannot replace lost solute. If the mark is overshot, follow the laboratory’s method for remaking the solution; removing some mixed solution does not restore the intended concentration.
Worked example 1
Find the concentration of a sodium carbonate standard
Problem
A student quantitatively transfers 1.325 g of anhydrous sodium carbonate into a 250.0 cm³ volumetric flask and makes the solution up to the mark. Its molar mass is 106.0 g mol⁻¹. Calculate the concentration.
Show full solution
Convert the transferred mass to amount
Method
Divide the measured mass by the molar mass.Reason
The known formula connects solute mass to amount in moles.Working
Answer
n(Na₂CO₃) = 1.325/106.0 = 0.01250 molUse the final volume
Method
Convert 250.0 cm³ to 0.2500 dm³, then divide the amount by this volume.Reason
The concentration belongs to the mixed solution at the mark, not to the water added.Working
Answer
c = 0.01250/0.2500 = 0.05000 mol dm⁻³
Quick check
Check your understanding 2 Use the mass transferred, then diagnose overfilling
A container with anhydrous sodium carbonate has a mass of 5.643 g before transfer and 4.317 g afterwards. All the transferred solid reaches a 250.0 cm³ flask. Using a molar mass of 106.0 g mol⁻¹, calculate the intended concentration. If the solution is made above the mark, how does its actual concentration compare with that value?
Show the steps Optional working
Show answer
The transferred mass is 5.643-4.317 = 1.326 g.
Overfilling leaves the same solute amount in a larger final volume, so the actual concentration is lower. Repeating titrations with this solution cannot restore its intended concentration.
Check your understanding 3 Can withdrawing solution undo overfilling?
A student dissolves 1.325 g of anhydrous Na₂CO₃ (molar mass 106.0 g mol⁻¹) but makes the final volume 252.0 cm³. After mixing thoroughly, the student withdraws 2.00 cm³ so 250.0 cm³ remains. Calculate the concentration of the remaining solution to three significant figures. Explain the effect of withdrawing the mixed solution in the next question.
Show answer
Before withdrawal, n = 1.325/106.0 = 0.01250 mol and c = 0.01250/0.2520 = 0.049603… mol dm⁻³. Uniform withdrawal leaves c unchanged, so the remaining concentration is 0.0496 mol dm⁻³ to three significant figures. It is below the intended 0.05000 mol dm⁻³.
Check your understanding 4 Explain the remaining solute
Explain why withdrawing 2.00 cm³ of the mixed solution above does not restore the intended concentration, even though the flask now contains 250.0 cm³.
Show answer
The removed portion has the same concentration as the rest, so it removes dissolved sodium carbonate as well as water. Both solute amount and solution volume fall in the same proportion; their ratio n/V stays unchanged. The remaining 250.0 cm³ contains less solute than was weighed. Check for both solute loss and the unchanged ratio in your explanation.
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Syllabus and review details
- GCE A-Level H2 Chemistry 2027 · 9476-2027
9476 (2027), complete syllabus
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