# How to Solve Law of Conservation of Mass Problems

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The Law of Conservation of Mass revolutionized the study of chemistry and is one of its most important principles. Although discovered by multiple researchers, its formulation is most often attributed to French scientist Antoine Lavoisier and is sometimes named after him. The law is simple: Atoms in a closed system can be neither created nor destroyed. In a reaction or series of reactions, the total mass of the reactants must equal the total mass of the products. In terms of mass, the arrow in a reaction equation becomes an equals sign, which is a great help when it comes to keeping track of quantities of compounds in a complex reaction.

#### TL;DR (Too Long; Didn't Read)

Balancing chemical equations recognizes that both sides of the equation must contain the same number of atoms of each element, so it's one way to solve for the conservation of mass. You can also use conservation of mass to find the masses of solutes in a solution.

## A Closed System

No matter can enter or escape a closed system, but energy may pass freely. The temperature inside a closed system can change, and a closed system can be irradiated by X-rays or microwaves. You do not have to consider the energy given off during an exothermic reaction or absorbed during an endothermic one when measuring mass before and after the reaction. Some compounds may change state, and some gases may be produced from solids and liquids, but the only parameter of importance is the total mass of all the compounds involved. It must stay the same.

## The Burning Log

The fact that a log weighs less after it burns was something of a mystery until scientists understood the principle of conservation of mass. Since mass can't be lost, it must transform into another form, and that's what happens. During combustion, the wood combines with oxygen to produce charcoal and soot, and it gives off gases such as carbon dioxide and carbon monoxide. You can calculate the total mass of these gases by weighing the log before burning and the solid carbon products remaining after the fire goes out. The difference in these weights must equal the total weights of the gases that go up the chimney. This is the basic idea behind the solution of all conservation of mass problems.

## Balancing Chemical Equations

A balanced chemical equation is one that demonstrates that atoms, like mass in general, are neither created nor destroyed during the reaction, which an equation describes. Balancing a reaction equation is one way of solving a conservation of mass problem. To do this, you recognize that both sides of the equation contain the same number of atoms of each element involved in the reaction.

For example, the unbalanced equation for rust formation, which is a combination of iron with oxygen to produce iron oxide, looks like this:

Fe + O2 --> Fe2O3

This equation isn't balanced because the two sides contain different numbers of iron and oxygen atoms. To balance it, multiply each of the reactants and the products by a coefficient that produces the same number of atoms of each element on both sides:

4Fe + 3O2 --> 2Fe22O3

Note that the number of atoms in a compound, represented by the subscripts in a chemical formula, never changes. You can only balance an equation by modifying coefficients.

## Solutes and Solutions

You don't necessarily have to know the chemical equation for a reaction to solve for the conservation of mass. For example, if you dissolve two or more compounds in water, you know that the masses of the ingredients must equal the total mass of the solution. As an example of how this can be useful, consider a student who weighs out particular weights of two compounds to add to a known amount of water and then spills a small amount of one of the compounds while transferring it to the solution. By weighing the final solution, the student can figure out exactly how much of the compound was lost.

## Conservation of Mass in Chemical Reactions

If certain reactants combine to produce known products and the balanced equation of the reaction is known, it's possible to calculate the missing mass of one of the reactants or products if all the others are known. For example, carbon tetrachloride and bromine combine to form dibromodichlormethane and chlorine gas. The balanced equation for this reaction is:

CCl4 + Br2 --> CBr2Cl2 + Cl2

If you know the masses of each of the reactants and can measure the mass of one of the products, you can calculate the mass of the other product. Similarly, if you measure the masses of the products and one of the reactants, you immediately know the mass of the other reactant.

## Example

A student combines 154 grams of carbon tetrachloride and an unknown quantity of bromine in a sealed container to produce 243 grams of dibromodichlormethane and 71 grams of chlorine. How much chlorine was used in the reaction, assuming the reactants are completely used u__p?

Since mass is conserved, we can set up an equality in which x represents the unknown quantity of bromine:

154g + x = 243g + 71g

x = the mass of bromine consumed in the reaction = 150 grams