What you'll be able to do: Determine the formula of a hydrate from heating data and evaluate whether a gravimetric result is trustworthy.
Best after: Empirical and Molecular Formulas, Percent Composition
Heating a hydrate drives off its water of crystallisation and leaves the anhydrous salt behind. Two balance readings are therefore enough to determine how many water molecules were bound to each formula unit. This lesson applies the empirical formula method to real laboratory data and asks the harder question of when that data can be believed.
These are recommended, not required. You can start this lesson at any time.
In CuSO₄ . 5 H₂O the dot is not multiplication in the usual sense, it records that five water molecules are built into each formula unit of the crystal. Those waters count fully in the molar mass, so the hydrate (249.68 g/mol) is much heavier per mole than the anhydrous salt (159.61 g/mol). The colour change from blue to white on heating is the visible sign that the water has gone.
CuSO₄ . 5 H₂O
Mass of water driven off = mass of hydrate minus mass of residue. Mass of anhydrous salt = mass of residue. Every gravimetric hydrate question reduces to those two lines, so write them down before doing any mole arithmetic. Remember to subtract the crucible mass from both readings first.
mwater = mhydrate - m_residue
Convert the water mass to moles using 18.02 g/mol, convert the residue mass to moles using the molar mass of the anhydrous salt, then divide moles of water by moles of salt. That quotient is x. Because x must be a whole number, a result of 4.87 rounds to 5, but a result of 3.4 is not a rounding problem, it is evidence of an experimental issue.
x = nwater / nanhydrous
Percent water = mass of water lost divided by hydrate mass, times 100. Compare it with the theoretical value calculated from the proposed formula. For CuSO₄ . 5 H₂O the theoretical figure is 5(18.02)/249.68 = 36.08 %. Agreement within a percent or so supports the formula; a large gap points to an error before the answer is reported.
Incomplete heating leaves water behind, so the measured water loss is too small and x comes out low. Overheating that decomposes the salt itself removes extra mass, so x comes out high. Spattering loses solid and also inflates the apparent water loss. A hygroscopic residue that reabsorbs moisture while cooling in open air lowers the apparent loss. Good practice is heating to constant mass and cooling in a desiccator.
This is the empirical formula method with the elements replaced by two components, water and the salt. If you can determine x here, you can determine any empirical formula from mass data, because the reasoning is identical.
Review: Empirical and Molecular FormulasAn ionic compound whose crystal includes a fixed number of water molecules per formula unit.
The bound water represented after the dot in a hydrate formula; it counts in the molar mass.
For a well-behaved hydrate, mass lost on gentle heating equals the mass of water driven off.
A non-integer x is evidence about the experiment, not a value to be reported as-is.
The method assumes the anhydrous salt is thermally stable at the temperature used. Salts that decompose break this assumption.
x = (mwater / 18.02) / (manhydrous / Manhydrous)
% H₂O = mwater / mhydrate x 100 %
A 4.98 g sample of hydrated copper(II) sulfate is heated to constant mass, leaving 3.18 g of white residue. Determine x in CuSO₄ . x H₂O.
Try it first: Which of the two masses is the water, and which is the salt?
0 of 4 steps revealed.
A student determines x = 3.4 for a hydrate expected to be the tetrahydrate. Give the most likely cause and its direction.
Try it first: Does an x that is too low mean too much or too little mass was lost?
0 of 3 steps revealed.
Why it's wrong: The residue is the anhydrous salt, so using the heavier hydrate molar mass understates its moles and inflates x.
Check instead: Match each mass to the substance it actually is before choosing a molar mass.
Why it's wrong: Both masses are then too large by the same amount, which distorts the mole ratio even though the difference is unaffected.
Check instead: Subtract the empty crucible mass from every reading first.
Why it's wrong: A hydrate has a fixed whole number of waters per formula unit, so a non-integer is evidence of experimental error.
Check instead: Round to the nearest whole number and explain the deviation, or identify the error if it is large.
Why it's wrong: It gives no chemical information and does not account for whether x came out high or low.
Check instead: Name the error and state which direction it pushes the measured mass loss.
Why it's wrong: The two are swapped, so the calculated ratio is inverted and x is far from any sensible value.
Check instead: Write mwater = mhydrate - m_residue explicitly before calculating.
No practice questions are available for this topic yet. You can still practice the whole unit.
Mass lost on heating is water, and mass remaining is the anhydrous salt. Convert each to moles, divide the moles of water by the moles of salt, and round to the nearest whole number to obtain the coefficient x in the formula. Systematic errors show up as an x that is far from a whole number.
Adapted from "Chemistry 2e" by OpenStax, Rice University, licensed CC BY 4.0. Changes were made. License