D. Quantities in Chemical Reactions · Quantities in Chemical Reactions

Investigation: Finding Percentage Composition in the Lab

D2.2 D3.1 A1.1 A1.4 A1.5 A1.6 A1.8 A1.10 A1.13About 75 minutes

Learning goals

I can plan and explain a lab that measures the percentage composition of a compound.
I can use the technique of heating to constant mass.
I can calculate percentage composition and percentage error from lab data.
I can identify sources of error and explain which way each one pushes the result.
I can follow safety rules and WHMIS information when heating chemicals.

Words to know

crucible
A small heat-resistant cup (porcelain or metal) used to heat solids strongly.

anhydrous
Without water: the solid left after the water of hydration has been driven off.

heating to constant mass
Heating, cooling and weighing repeatedly until two weighings in a row agree (for example within 0.002 g), which shows the change is complete.

theoretical value
The value expected from theory, such as a percentage calculated from the formula.

percentage error
|experimental value − theoretical value| ÷ theoretical value × 100%.

systematic error
An error that pushes every result in the same direction, such as an incomplete reaction.

WHMIS
Workplace Hazardous Materials Information System: Canada's system of hazard pictograms, labels and safety data sheets (SDS).

Can you prove a formula with a balance?

In the last lesson you calculated that magnesium oxide, MgO, is 60.31% magnesium by mass, and that blue copper sulfate crystals, CuSO₄·5H₂O, are 36.08% water. Those numbers came from formulas. In this investigation you test them with real measurements. If the law of definite proportions is right, careful lab work should give the same percentages, apart from experimental error.

Two classic investigations

Investigation A: Magnesium oxide. A strip of magnesium ribbon of known mass is heated in a crucible. It reacts with oxygen in the air: 2Mg(s) + O₂(g) → 2MgO(s). The lid is lifted a little now and then to let air in, but kept mostly on so that white MgO smoke does not escape. The product is weighed. Then:

% Mg = mass of Mg ÷ mass of MgO × 100%

Investigation B: Water in a hydrate. Blue copper(II) sulfate pentahydrate is heated gently. The water of hydration leaves as steam, and white anhydrous copper(II) sulfate is left: CuSO₄·5H₂O(s) → CuSO₄(s) + 5H₂O(g). Then:

% water = (mass before − mass after) ÷ mass before × 100%

Both labs use the same equipment and the same key technique: heating to constant mass.

Crucible set-up. The crucible sits in a clay triangle on an iron ring. The lid is kept slightly open so air can get in. (Not to scale.)

Safety first (A1.4)

These investigations are done in a school lab with a teacher, never at home.

Wear safety goggles; tie back long hair; keep sleeves and papers away from the flame.
Do not look directly at burning magnesium: it gives off a very bright light that can hurt your eyes.
Handle the crucible and lid only with crucible tongs. A hot crucible looks exactly like a cold one. Let it cool on a heat-resistant pad.
Copper(II) sulfate is harmful if swallowed and toxic to aquatic life. Its WHMIS label and safety data sheet (SDS) say how to handle and dispose of it; never pour it down the sink unless your teacher says so.
Weigh crucibles only when they are cool: a hot object makes air rise around the balance and gives a false reading.

Planning (A1.1)

A good investigation starts with a testable question and a hypothesis:

Question: What is the percentage of water by mass in copper(II) sulfate pentahydrate?
Hypothesis: If the formula CuSO₄·5H₂O is correct, then heating the crystals to constant mass will show that 36.1% of their mass is water, because 5 mol of water (90.10 g) is lost from each 249.72 g of hydrate.

Plan your data table before you start, with a row for every mass you will measure and room for repeat weighings.

Measurement (Investigation B)	Mass (g)
empty crucible + lid	18.235
crucible + lid + hydrate (before heating)	20.735
after heating 1 (cooled)	19.861
after heating 2 (cooled)	19.842
after heating 3 (cooled)	19.840

Sample data. The last two weighings differ by only 0.002 g, so the water is all gone.

Heating to constant mass. The mass drops a lot after the first heating, a little after the second, and almost not at all after the third. Only then can you be sure all the water has been driven off.

Worked example

Example 1: Analysing the hydrate data

Use the sample data table to find the percentage of water and the percentage error.

Mass of hydrate = 20.735 − 18.235 = 2.500 g
Mass of anhydrous CuSO₄ = 19.840 − 18.235 = 1.605 g
Mass of water lost = 2.500 − 1.605 = 0.895 g
% water = 0.895 ÷ 2.500 × 100% = 35.8%
Theoretical % water = 90.10 ÷ 249.72 × 100% = 36.08%
% error = |35.8 − 36.08| ÷ 36.08 × 100% = 0.78%

Experimental: 35.8% water, a percentage error of about 0.8%. The result is a little low.

Bar model of Example 1. The mass that disappears on heating is the water.

Worked example

Example 2: Analysing magnesium oxide data

A student heats 0.300 g of magnesium ribbon in a crucible and gets 0.485 g of white product. Find the percentage of magnesium and the percentage error. Is the result high or low?

% Mg = 0.300 ÷ 0.485 × 100% = 61.86% ≈ 61.9%
Theoretical (MgO) = 24.31 ÷ 40.31 × 100% = 60.31%
% error = |61.9 − 60.31| ÷ 60.31 × 100% = 2.6%
The experimental value is high. That means the product weighed too little for the amount of magnesium.

61.9% Mg, a 2.6% error, too high.

Sources of error (A1.8)

A good conclusion does not just say "human error". It names a specific cause and says which way it pushes the result.

For the magnesium lab:

Some magnesium did not react (the ribbon was coated or not heated long enough). The product is too light, so % Mg is too high.
White MgO smoke escaped when the lid was lifted. The product is too light, so % Mg is too high.
Magnesium reacted with nitrogen in the air to form magnesium nitride, Mg₃N₂, which is 72.2% Mg. Some product is lighter than MgO would be, so % Mg is too high. (Many procedures add a few drops of water and reheat, which turns the nitride into magnesium oxide.)

For the hydrate:

Not heated to constant mass: some water stays, so % water is too low.
Overheating: copper(II) sulfate can start to decompose and lose more than water, so % water is too high.
Crucible absorbs moisture from the air while cooling: the final mass is too high, so % water is too low. Cooling with the lid on helps.

Writing the conclusion (A1.10)

Answer the question, state your result with its percentage error, compare it with the hypothesis, and name the most likely source of error and its direction. Example: "The hydrate was 35.8% water, 0.8% below the theoretical value of 36.08%. This supports the formula CuSO₄·5H₂O. The low result was most likely caused by a small amount of water remaining in the crystals; a fourth heating would test this."

Just for fun

Why do chemists trust crucibles with their most important jobs?

Because a crucible can really take the heat.

Hands-on activity

Percentage of water in an apple (heating to constant mass at home)

This kitchen version uses the same method as the hydrate lab. A grown-up must handle the oven and hot trays.

You need: an apple, a knife and cutting board (grown-up help), a baking tray lined with parchment paper, a kitchen scale, oven mitts.

Have a grown-up slice the apple into thin rings (about 3 mm). Weigh the parchment, then the parchment with the slices. Record the starting mass of apple.
Bake at a low temperature (about 90 °C, or the oven's lowest setting) for 1 hour. Let the tray cool for 10 minutes, then weigh.
Bake for another 30 minutes, cool and weigh again. Repeat until two weighings in a row differ by 1 g or less: constant mass.
Calculate % water = mass lost ÷ starting mass × 100%.
Explain one source of error and its direction.

What to look for: apples are mostly water, so you should lose most of the mass (often 80% to 85% or more). Possible errors: the slices were not fully dry (result too low) or some edges burned, losing more than water (result too high). An apple is a mixture, so different apples give different percentages; unlike a pure hydrate, it has no fixed composition. Enjoy the apple chips!

Your turn

A student heats 0.243 g of magnesium and gets 0.391 g of product. Find the percentage of Mg and the percentage error.

Why must you heat to constant mass instead of heating just once?

A 5.00 g sample of a hydrate weighs 3.20 g after heating to constant mass. What percentage of the hydrate is water?

Name two sources of error that would make the percentage of magnesium in the MgO lab too high, and explain why.

List three safety precautions for heating a crucible.

Write a testable question and a hypothesis for the magnesium oxide investigation.

More practice: warm-up

Write the formula for percentage error.

What does anhydrous mean?

Why is the crucible lid kept mostly on while magnesium burns?

What does "constant mass" mean?

How many significant figures are in a mass of 0.895 g?

More practice: on your own

Find the percentage error in Example 2 if the theoretical value is 60.31% and the student's value is 61.86% (use the unrounded value).

Epsom salt is MgSO₄·7H₂O (M = 246.52 g/mol). Find the theoretical percentage of water. A student measures 47.9%. Find the percentage error and suggest the most likely cause.

Design a data table for Investigation A (magnesium oxide).

A student starts with 0.360 g of Mg and obtains 0.597 g of product. Does the result support the formula MgO?

Explain why the crucible must be weighed cool, not hot.

Challenge

In the hydrate lab, a student weighs the crucible while it is still hot after the last heating. Will the calculated percentage of water be too high or too low? Explain.

A 2.000 g sample of hydrated barium chloride, BaCl₂·xH₂O, leaves 1.705 g of anhydrous BaCl₂ (M = 208.23 g/mol) after heating. Find x.

In the apple activity, a 120.0 g sample dried to 17.5 g. Find the percentage of water. Can this be called the "percentage composition of an apple" in the same sense as for CuSO₄·5H₂O? Explain.

Check your understanding

Quiz

Why is a hydrate heated to constant mass?

A 3.000 g hydrate sample weighs 1.920 g after heating to constant mass. What is the percentage of water?

An experimental value is 58.0% and the theoretical value is 60.0%. What is the percentage error?

In the MgO lab, white smoke escapes from the crucible. How does this affect the calculated % Mg?

Which is the safest way to handle a crucible after heating?

A hydrate is not heated long enough. How does this affect the percentage of water found?

For parents and teachers

Big idea: This is the inquiry for expectation D2.2 (percentage composition), and it practises many scientific-investigation skills from strand A: a testable question and hypothesis (A1.1), safety and WHMIS (A1.4), careful procedure and data recording (A1.5, A1.6), error analysis (A1.8), conclusions (A1.10) and significant figures (A1.13).

Safety at home: The magnesium and copper sulfate investigations are school-lab only. The apple activity is the home version; a grown-up should handle the knife and oven.

How to help: Ask your teen to explain why each step is done (lid on, cooling before weighing, repeated heating). When they name a source of error, ask "Would that make your answer too big or too small?" That question is the heart of a good lab conclusion.

Common difficulties:

Subtracting the wrong masses (forgetting to subtract the crucible).
Writing "human error" instead of a specific, directional source of error.
Mixing up which direction an error pushes a ratio (a lighter product makes % Mg higher).
Reporting too many or too few significant figures; a balance reading of 0.001 g sets the precision.