Verifying chemical laws

A chemistry teacher hands you a table of masses from a real experiment and asks one question: does it obey the law you were taught? The laws of chemical combination — conservation of mass, definite proportions, multiple proportions — are not abstract slogans. They are testable claims about numbers, and testing them is a specific arithmetic skill: computing the right ratio, scaling one data set so it lines up with another, and reading whether the result is constant or a small whole number. This article works through that skill using the ISC Class 11 "Some Basic Concepts of Chemistry" data, staying entirely within mass ratios and whole-number checks — no gas laws, no mole calculations beyond simple ratios.

The core insight

Verifying a law of chemical combination means computing a defined mass ratio from experimental data and checking whether it is constant across samples (definite proportions), reduces to small whole numbers across compounds (multiple proportions), or balances input against output (conservation of mass).

The core idea

Every verification exercise reduces to the same three moves: identify which masses belong to which element or compound, put them on a common footing so different experiments can be compared fairly, and check the resulting ratio against the pattern the law predicts.

Conservation of mass asks whether the total mass entering a reaction equals the total mass leaving it. In a closed system, nothing is created or destroyed — atoms only rearrange.

\sum m_{\text{reactants}} \overset{?}{=} \sum m_{\text{products}}

where: $m_{\text{reactants}}$ is the sum of all masses fed into the reaction and $m_{\text{products}}$ is the sum of all masses recovered afterward, including any unreacted excess and any gas evolved if it can be captured and weighed.

Definite proportions asks whether the same compound, however it is prepared or sourced, always contains its constituent elements in the same mass ratio.

\left(\frac{m_A}{m_B}\right)_{\text{sample 1}} \overset{?}{=} \left(\frac{m_A}{m_B}\right)_{\text{sample 2}}

where: $m_A$ and $m_B$ are the masses of the two elements in a given sample of the compound, and the two samples are independent — different batches, different sources, even different laboratories.

Multiple proportions compares two different compounds built from the same pair of elements. Fix the mass of one element at a common reference value in both compounds, then compare the masses of the second element.

\frac{m_B\ \text{in compound 1 (per fixed } m_A)}{m_B\ \text{in compound 2 (per fixed } m_A)} = \text{small whole-number ratio}

where: $m_A$ is scaled to the same value in both compounds before the comparison, and $m_B$ is the mass of the other element that combines with it in each case. The scaling step is the one place students slip. Raw experimental masses from two trials are almost never at the same reference mass, so before any ratio can be trusted, one data set must be scaled by a single multiplying factor — never added to or subtracted from — until the chosen element's mass matches across both trials.

Figure

Three data tables feeding three different comparison arrows labelled conservation definite and multiple proportions

Derivation AScaling one data set to a common reference mass so two experiments can be compared

The goal is to show, from raw masses that were never measured on the same scale, exactly how to build the single multiplying factor that converts one experiment's data onto the same reference mass as the other, so that a ratio comparison between them is legitimate rather than an accident of how much material happened to be used in each trial.

Step 1. Write down the masses actually measured in each experiment for the element chosen as the reference, call them $m_{A,1}$ (experiment 1) and $m_{A,2}$ (experiment 2). These will almost never be equal, because the two experiments used different quantities of starting material.

Step 2. Choose a target reference mass $m_A^{*}$ — often the smaller of the two, or a round number that divides evenly into both, so the arithmetic stays clean.

Step 3. Compute a scale factor for each experiment separately: $k_1 = m_A^{*} / m_{A,1}$ and $k_2 = m_A^{*} / m_{A,2}$ . Multiply every mass in an experiment's data set by that experiment's own $k$ — the reference element's mass, the other element's mass, and the compound's total mass all get multiplied by the same factor, because scaling represents "if I had used this much material instead," not a change in composition.

Step 4. After scaling, both experiments now report masses for the same amount of the reference element. Only now is it valid to compare the other element's scaled mass across the two experiments — either checking it is equal (definite proportions) or forming its ratio and reducing to lowest terms (multiple proportions).

Worked example

Copper forms two chlorides. Analysis of the first shows $6.35\ \text{g}$ of copper combining with $3.55\ \text{g}$ of chlorine. Analysis of the second shows $3.175\ \text{g}$ of copper combining with $3.55\ \text{g}$ of chlorine. Verify whether these data obey the law of multiple proportions.

Step 1 — Choose the reference mass. Fix copper at a common value. The smaller copper mass, $3.175\ \text{g}$ , is convenient since the first sample's copper mass is exactly double it.

Step 2 — Scale the first sample down to $3.175\ \text{g}$ of copper. The scale factor is $k = 3.175 / 6.35 = 0.5$ . Scaling the chlorine mass by the same factor:

m_{\text{Cl}}\ (\text{scaled}) = 3.55 \times 0.5 = 1.775\ \text{g}

So $3.175\ \text{g}$ of copper combines with $1.775\ \text{g}$ of chlorine in the first chloride, once scaled.

Step 3 — Read off the second sample (already at $3.175\ \text{g}$ Cu). $3.175\ \text{g}$ of copper combines with $3.55\ \text{g}$ of chlorine in the second chloride.

Step 4 — Compare the two chlorine masses for the same fixed copper mass.

\frac{m_{\text{Cl}}\ \text{in chloride 2}}{m_{\text{Cl}}\ \text{in chloride 1 (scaled)}} = \frac{3.55}{1.775} = 2:1

Step 5 — Conclusion. The ratio $2:1$ is a small whole number, so the data obey the law of multiple proportions: for the same fixed mass of copper, the two chlorides contain chlorine in a simple whole-number ratio. The verified ratio is $2:1$ , consistent with the compounds $\text{CuCl}$ and $\text{CuCl}_2$ .

Common traps

Comparing raw, unscaled masses straight across two experiments instead of first fixing one element's mass at a common reference value — the single most frequent error in this topic.
Verifying conservation of mass while forgetting a gas evolved or an unreacted excess reactant, especially in an open system where a product escapes unmeasured.
Rounding a ratio too early and missing that it reduces to a small whole number — carry extra decimal places before concluding a ratio is "not whole-number."
Confusing which law is being tested: definite proportions compares the same compound across independent samples, while multiple proportions compares different compounds of the same two elements.

Ask the tutor: Have a data table you want checked against a law of chemical combination, or need help choosing the reference element for a multiple-proportions problem? Ask the AI tutor to work through it with you.

Why do we scale one data set instead of just dividing the two ratios directly?

Because the two experiments were rarely run with the same starting quantities, the raw masses of the fixed element differ between them. If you compare the other element's mass directly without first putting the fixed element on equal footing, you are comparing amounts, not composition — the numbers would carry information about how much material was used, not about the fixed whole-number pattern the law predicts. Scaling by a single multiplying factor removes that "how much was used" variable so only the composition ratio remains.

Does the law of conservation of mass still hold if a gas escapes during the reaction?

The law itself always holds — mass is never actually created or destroyed. What can go wrong is your verification of it: if the reaction is open to the air and a gas product escapes before you weigh the products, your measured product mass will appear less than the reactant mass, making it look like mass was lost. To verify conservation of mass correctly, either work in a sealed, closed system so nothing escapes, or account for the escaped gas by calculating its mass separately and adding it back in.

How do I know which element to fix as the reference when checking multiple proportions?

Either element works in principle, but pick whichever one makes the arithmetic simplest — usually the element whose two masses across the compounds share an easy common multiple, so the scale factor comes out as a clean number like $0.5$ or $2$ . Look at both elements' masses before choosing; picking the awkward one only makes the scaling step messier, it never changes the final whole-number ratio you arrive at.

Verifying chemical laws

The core idea

Worked example

Common traps

Before this

Where this leads