E. Solutions and Solubility · Solutions and SolubilityPreparing Standard Solutions and Dilutions
E2.3 E2.2 A1.4 A1.5 A1.13About 70 minutes
Learning goals- I can describe how to prepare a standard solution of known concentration from a solid, using a balance and a volumetric flask.
- I can use c₁V₁ = c₂V₂ to plan and calculate dilutions.
- I can choose suitable glassware and follow safe practice (including WHMIS and adding acid to water).
- I can explain how precision of equipment affects the significant digits of a concentration.
Words to know
standard solution
A solution whose concentration is known precisely.
stock solution
A concentrated solution kept on hand and diluted to make the solutions needed.
dilution
Lowering a solution's concentration by adding more solvent; the amount of solute stays the same.
volumetric flask
A flask with a single etched line marking one exact volume (e.g. 100.0 mL or 250.0 mL).
volumetric (transfer) pipette
A pipette that delivers one exact volume, e.g. 10.00 mL or 25.00 mL.
meniscus
The curved surface of a liquid in a narrow tube; for water, read the bottom of the curve at eye level.
WHMIS
Workplace Hazardous Materials Information System: Canada's system of labels, pictograms and safety data sheets (SDS) for hazardous products.
Recipes with precision
A pharmacist preparing a child's medicine, a water treatment operator adjusting chlorine, and a lab technician testing a lake sample all have the same job: make a solution of exactly the right concentration. There are two ways to do it:
- Dissolve a measured mass of solid solute and make it up to an exact volume.
- Dilute a more concentrated stock solution.
This lesson describes both, as you would do them in a school lab, and the calculations behind them.
Lab safety and WHMIS (A1.4)
Before using any chemical, read its WHMIS 2015 label and safety data sheet (SDS). Wear safety goggles; use a lab coat and gloves when a label says so. Many stock solutions in a chemistry lab (acids, bases, silver nitrate) are corrosive or toxic. These procedures are done in a school lab with a teacher, never at home with lab chemicals.
Method 1: preparing a standard solution from a solid
- Calculate the mass of solute: n = c × V, then m = n × M.
- Weigh that mass on an electronic balance, using a clean, dry beaker or weighing boat.
- Dissolve the solid in a beaker with about half the final volume of distilled water. Stir until fully dissolved.
- Transfer the solution to a volumetric flask of the right size through a funnel. Rinse the beaker, stirring rod and funnel with small amounts of distilled water and add the rinsings to the flask, so no solute is lost.
- Fill to the line: add distilled water until the bottom of the meniscus sits exactly on the etched line (use a dropper for the last few millilitres; read at eye level).
- Stopper and invert the flask about 10 to 15 times to mix completely.
- Label it: name, formula, concentration, date and your name.
Method 2: dilution
When you add water to a solution, the amount of solute (n) does not change; it just spreads through a larger volume. Since n = c × V:
n before = n after → c₁V₁ = c₂V₂
- c₁, V₁: concentration and volume of the concentrated (stock) solution you take
- c₂, V₂: concentration and final total volume of the diluted solution
V₁ and V₂ can be in any volume unit, as long as both use the same unit.
Procedure: use a volumetric pipette (with a pipette bulb, never by mouth) to transfer V₁ of the stock solution into a volumetric flask of volume V₂, then fill to the line with distilled water, stopper and invert.
Diluting acids: always add acid to water, never water to concentrated acid. Mixing concentrated acid with water releases a lot of heat; if a little water is added to a lot of acid, it can boil and spatter acid. Many students remember: "Do as you oughta, add acid to water."
Worked exampleExample 1: Dilution calculations
(a) 25.0 mL of 2.00 mol/L NaOH is diluted to 500.0 mL. Find the new concentration. (b) What volume of 12 mol/L concentrated HCl is needed to make 1.00 L of 0.50 mol/L HCl? (c) How much water must be added to 50.0 mL of 1.00 mol/L CuSO₄ to make it 0.250 mol/L?
- (a) c₂ = c₁V₁ ÷ V₂ = (2.00 mol/L)(25.0 mL) ÷ 500.0 mL = 0.100 mol/L.
- (b) V₁ = c₂V₂ ÷ c₁ = (0.50 mol/L)(1.00 L) ÷ 12 mol/L = 0.0417 L ≈ 42 mL (two significant digits). In the lab: put about 500 mL of water in the 1 L flask, add the 42 mL of acid slowly, then fill to the line.
- (c) V₂ = c₁V₁ ÷ c₂ = (1.00)(50.0) ÷ 0.250 = 200 mL total. Water to add = 200 − 50.0 = 150 mL. (V₂ is the total volume, not the water added.)
(a) 0.100 mol/L; (b) about 42 mL; (c) add 150 mL of water.
Worked exampleExample 2: Planning a standard solution
Describe how to make 250.0 mL of 0.200 mol/L potassium nitrate (KNO₃, M = 101.11 g/mol), including the mass and the equipment.
- n = c × V = 0.200 mol/L × 0.2500 L = 0.0500 mol.
- m = n × M = 0.0500 mol × 101.11 g/mol = 5.06 g.
- Equipment: electronic balance, weighing boat, 150 mL beaker, stirring rod, wash bottle of distilled water, funnel, 250.0 mL volumetric flask with stopper, dropper, label.
- Steps: weigh 5.06 g KNO₃; dissolve in about 100 mL distilled water; transfer to the flask with rinsings; fill to the line (bottom of meniscus at eye level); stopper and invert 10 to 15 times; label.
Dissolve 5.06 g of KNO₃ and make it up to exactly 250.0 mL in a volumetric flask.
Serial dilution
To make very dilute solutions (for example, standards for testing a lake at the ppm level), chemists dilute in steps. Diluting 10.00 mL to 100.0 mL is a 1 in 10 (tenfold) dilution. Doing that three times in a row gives 10 × 10 × 10 = a 1000-fold dilution, which is far more accurate than trying to measure 0.1 mL once.
Precision and significant digits (A1.13)
A 250.0 mL volumetric flask is accurate to about ±0.1 mL, while a 250 mL beaker's markings may be off by 5% or more. That is why concentrations made in volumetric glassware can be reported to three or four significant digits, and those made in beakers cannot.
Just for funChemists have a rhyme for the safe way: "Do as you oughta, add acid to water." Nobody bothered writing a rhyme for the other order, because what you get is spattering, not poetry.
Hands-on activityKitchen serial dilution of a drink mix
You need: a coloured drink crystal or juice concentrate, a measuring cup, a 15 mL tablespoon, 4 clear glasses, water, and a white sheet of paper.
- Make a 'stock' by dissolving 1 tablespoon of drink crystals in 150 mL of water (or use undiluted juice concentrate).
- Glass A: 15 mL of stock + 135 mL water (total 150 mL). This is a 1 in 10 dilution.
- Glass B: 15 mL from A + 135 mL water. Glass C: 15 mL from B + 135 mL water.
- Line up the stock, A, B and C on white paper and compare colours.
- Use c₁V₁ = c₂V₂ to show that each glass is one-tenth as concentrated as the one before, and find C's concentration as a fraction of the stock.
What to look for: each glass is noticeably paler; C is 1/1000 of the stock concentration (10 × 10 × 10). Explain why the total volume (150 mL), not the water added (135 mL), is V₂. You may drink the diluted juice, as long as everything used was clean kitchen equipment.
Your turn
110.0 mL of 6.0 mol/L HCl is diluted to 250.0 mL. Find the new concentration.
c₂ = (6.0)(10.0) ÷ 250.0 = 0.24 mol/L.
2What volume of 2.00 mol/L stock is needed to make 100.0 mL of 0.500 mol/L solution?
V₁ = (0.500)(100.0) ÷ 2.00 = 25.0 mL.
3To what final volume must 40.0 mL of 0.800 mol/L KCl be diluted to make 0.200 mol/L?
V₂ = (0.800)(40.0) ÷ 0.200 = 160 mL.
4In the last question, how much water is added?
5What mass of NaCl is needed for 100.0 mL of 0.150 mol/L solution? (58.44 g/mol)
n = 0.0150 mol; m = 0.0150 × 58.44 = 0.877 g.
6Why do we dissolve the solid in a beaker before putting it in the volumetric flask?
It is easier to dissolve completely in a beaker (and to stir), and the solid could block the narrow neck. Rinsing the beaker into the flask keeps all of the solute.
7Why must you add acid to water and not water to acid?
Mixing releases a lot of heat. Adding water to concentrated acid can make the small amount of water boil and spatter acid. Adding acid slowly to a large volume of water spreads out the heat.
More practice: warm-up
1When a solution is diluted, which quantity stays the same: c, V or n?
2Where do you read the volume on a meniscus of water?
At the bottom of the curve, at eye level.
3Name the piece of glassware used to make up an exact final volume.
4What does WHMIS stand for?
Workplace Hazardous Materials Information System.
5A 1 in 10 dilution of 0.50 mol/L gives what concentration?
More practice: on your own
1A student needs 500.0 mL of 0.0200 mol/L CuSO₄. She has 0.500 mol/L stock. Describe the dilution, including the volume of stock.
V₁ = (0.0200)(500.0) ÷ 0.500 = 20.0 mL. Use a 20.00 mL (or 10.00 mL twice) volumetric pipette to transfer stock into a 500.0 mL volumetric flask partly filled with distilled water, fill to the line, stopper and invert.
2Three successive 1 in 10 dilutions are made from 0.100 mol/L stock. What is the final concentration?
0.100 ÷ 1000 = 1.00 × 10⁻⁴ mol/L.
3A student fills a volumetric flask so that the top of the meniscus touches the line. Is the final concentration too high or too low? Explain.
Too high. Too little water was added (the bottom of the meniscus is below the line), so the volume is less than intended and c = n/V is larger.
4Describe two errors that would make a standard solution's concentration lower than calculated.
Examples: solute lost (spilled, or the beaker was not rinsed into the flask); too much water (filled above the line); solid was damp so less actual solute was weighed.
5Why is a serial dilution more accurate than diluting 0.10 mL of stock to 100.0 mL in one step?
Measuring a tiny volume like 0.10 mL has a large percentage error. Each step of a serial dilution uses volumes (e.g. 10.00 mL) that can be measured precisely.
Challenge
1A lab has 18 mol/L sulfuric acid. Describe, with calculations and safety steps, how to make 2.00 L of 0.45 mol/L H₂SO₄.
V₁ = (0.45)(2.00 L) ÷ 18 = 0.050 L = 50 mL. Wearing goggles, gloves and apron in a fume hood: put about 1.5 L of distilled water in a 2 L volumetric flask (or beaker, cooled), slowly add the 50 mL of acid to the water while swirling, let it cool to room temperature, then fill to the 2.00 L line and mix.
250.0 mL of 0.300 mol/L NaCl and 150.0 mL of 0.100 mol/L NaCl are mixed. Find the final concentration.
n = (0.300)(0.0500) + (0.100)(0.1500) = 0.0150 + 0.0150 = 0.0300 mol; V = 0.2000 L; c = 0.150 mol/L.
3You need 100.0 mL of 0.0500 mol/L NaCl but only have a 0.01 g balance. Show why it would be better to make 250.0 mL of 0.500 mol/L stock and dilute it, rather than weighing the solid directly for 100.0 mL.
Direct: m = 0.00500 mol × 58.44 = 0.292 g; a ±0.01 g balance gives about ±3% error. Stock: m = 0.125 mol × 58.44 = 7.31 g, only about ±0.14% error. Then dilute 10.00 mL of stock to 100.0 mL (c₂ = 0.500 × 10.00/100.0 = 0.0500 mol/L) using precise volumetric glassware.
Quiz
2. 20.0 mL of 1.50 mol/L HCl is diluted to 300.0 mL. The new concentration is
3. Which glassware gives the most precise final volume of 250.0 mL?
4. When diluting concentrated acid, you should
5. What mass of NaOH (40.00 g/mol) is needed to make 250.0 mL of 0.100 mol/L?
6. After a dilution, which is true?
Big idea (E2.3): standard solutions are made by dissolving a weighed solid in a volumetric flask, or by diluting a stock solution using c₁V₁ = c₂V₂.
How to help: Ask your teen to talk you through the steps for making a solution, as if you were the lab partner. Listen for: calculate, weigh, dissolve, transfer and rinse, fill to the line at eye level, invert, label. During the kitchen dilution, ask which volume is V₂.
Common difficulties:
- Using the volume of water added as V₂ instead of the final total volume.
- Mixing units (mL for one volume and L for the other).
- Forgetting to rinse glassware into the flask, or reading the top of the meniscus.
Safety: concentrated acids, bases and other lab stock solutions are for a supervised school lab only. The home activity uses only drink mix and water.