A short story about the birth of the Law of conservation of mass
It took them only an instant to cut off that head, and a hundred years may not produce another like it. - Joseph-Louis Lagrange
Joseph-Louis Lagrange, a French mathematician, made these statements when Antoine Laurent Lavoisier was beheaded as a result of the French Revolution, as he was a tax collector working for the French government.
How is Antoine Lavoisier related to chemistry, you may ask?
Apart from being a tax collector, Antoine Lavoisier was a French chemist who laid the foundation for modern-day chemistry through many discoveries like what happens when things burn (Combustion theory). He also investigated the composition of water and synthesised pure water by chemically combining hydrogen and water. Through this discovery, Lavoisier concluded that water is not an element but a compound of two substances.
Lavoisier's wife, Marie Lavoisier, was equally enthusiastic about science. She was also good at languages and translated all of her husband's work into English.
Lavoisier's experimental methods set an example for the community and aspiring chemists that quantitative measurement is the heart of chemistry. He, through his various quantitative measurements, elucidated that the mass of the substance remains the same before and after the chemical reaction, where nothing is lost and nothing is gained. This is called the law of conservation of mass and Lavoisier is the man behind it, which is why we are telling you his story today.
He authored the first modern chemistry book, which compiled all the knowledge of chemistry that was known until that point in time. Lavoisier's book, named Traité élémentaire de Chimie which translates to "Elements of Chemistry," was published in the year 1789.
Following his death, Marie Lavoisier published all of her husband's lab notes and findings. She thus ensured that Lavoiser's name is never forgotten and his contribution to chemistry is forever remembered and celebrated.[2] Her noble mission had been accomplished, and now Lavoisier is regarded as the father of modern chemistry.
As Joseph-Louis Lagrange aptly remarked, it's been more than 100 years and another head like that of Lavoisier's is not born.
Fig. 1 - A portrait of Antonie Lavoisier and Mary Lavoisier.
- We will introduce you to the definition of conservation of mass.
- Then, we will look into a few examples of chemical reactions where mass is conserved while discussing open and closed systems and how the law of conservation of mass is applicable to both.
- We will work out some calculations based on the law of conservation of mass.
- We will experimentally verify the law of conservation of mass.
- Likewise, we will then deep dive into the expression of conservation of mass.
Conservation of Mass Definition
We can define the law of conservation of mass in the following way:
The law of conservation of mass states that in a closed system matter can neither be created nor destroyed, it can only change forms.
In other words, no atoms can be created or lost during a chemical reaction, meaning the mass of each reactant is equal to the total mass of the product.
All the atoms combine to produce products. Therefore, in any balanced chemical equation, the number of atoms on the LHS of the equation is always equal to the number of atoms on the RHS of the equation.
As the number of atoms remains the same, the sum of the masses of the reactants will be equal to the sum masses of the products in a reaction. Also, the sum of the relative formula masses of the reactants will be equal to the sum of the relative formula masses of the products.
In simple terms, mass is conserved during a chemical reaction.
Conservation of Mass Examples
Consider the following algebraic expression:
\[6x + 4y = 24\]
where
\[ x=2 \text{ and } y = 3.\]
Both sides of the equation have the same mathematical value.
Let us adapt the same concept to chemical equations, so consider
\[2H_2+O_2\rightarrow 2H_2O.\]
If we count the number of hydrogen and oxygen atoms on either side of the chemical equation, we will arrive at the conclusion that the number of atoms remains the same. This holds true, always, almost in any kind of chemical equation.
Now, since we are speaking of masses, let us understand how mass remains the same by this simple calculation. To calculate the total formula masses of reactants and products, we need the relative atomic masses of the atoms involved.
\[A_r \text { of hydrogen = 1}\]
\[A_r \text { of oxygen = 16}\]
The molecular mass of hydrogen:
\[H_2 = 1 \times 2 = 2.\]
The molecular mass of oxygen:
\[O_2 = 2 \times 16 = 32.\]
On the LHS,
\begin{align} 2H_2+O_2 = & (2 \times 2) + 32 \\ = &4+32 \\ = &36 \end {align}
On the RHS,
\begin{align} 2H_2O = & (2 \times 18) \\ =& 36 \end {align}
Thus, the sum of the relative formula masses on either side is \(36\). Do we now understand how the mass is conserved?
Open and closed systems
There is a little problem with some kinds of chemical reactions where gases are involved.
Let us consider the following reaction where gas is involved. Calcium carbonate, on heating, decomposes to calcium oxide and carbon-dioxide:
\[ CaCO_3\xrightarrow{\text{heat}} CaO + CO_2.\]
If this experiment is not performed in a closed system, the carbon-dioxide, being a gas, escapes, and we might quickly assume that the mass is not conserved. This is because we have not managed to trap the gas and weigh it along with the calcium oxide produced. As a result, there will be a difference in the initial and final masses where we notice a decrease in the mass.
Alternatively, if you perform the same experiment in a closed system, we can include the mass of the carbon-dioxide gas produced, and we will understand that the total mass does not change at the end of the reaction.
Similarly, if a metal like magnesium ribbon is burnt in the air, we get magnesium oxide as the product which weighs more than the magnesium ribbon taken at the start of the reaction. This is because, when magnesium burns, it reacts with the oxygen in the air, which cannot be measured by a balance. If that oxygen from the atmosphere is not considered, we might assume that this reaction resulted in an increase in the mass:
However, mass is conserved in this reaction as well. If we can somehow measure the oxygen reacted by performing this in a closed system, we'll be able to verify and prove that the law of conservation of mass holds true.
As the weights of gas in most cases, whenever we are discussing the law of conservation of mass, we are often referring to closed systems where all the products are recovered and measured.
Conservation of Mass Calculations
Let us now look into some of the example calculations to understand how mass is conserved in a chemical reaction.
Question 1:
\(78 \, \mathrm{g}\) of magnesium oxide is produced when \(38 \, \mathrm{g}\) of magnesium reacts with \( X \, \mathrm{g}\) of oxygen. Find the value of \(X\).
Calculation:
Let us write a simple word equation for this question
\[ \mathrm{Magnesium} + \mathrm{Oxygen} \rightarrow \mathrm{Magnesium \, oxide}. \]
As we are not calculating the formula masses, we don't have to write an actual balanced equation, so plugging in the values gives us
\begin{align} 38 \, \mathrm{g} + X \, \mathrm{g} & =78 \, \mathrm{g} \\ X \, \mathrm{g} &= 78 \, \mathrm{g}-38 \, \mathrm{g} \\ X \, \mathrm{g} &= 40 \, \mathrm{g}. \end{align}
Using the law of conservation of mass, we can estimate the unknown amount of a reactant or a product.
Question 2:
An unknown amount of calcium carbonate is heated in a sealed system. \( 38 \, \mathrm{g}\) of calcium oxide and \(32 \, \mathrm{g}\) of carbon-dioxide are produced. Calculate the amount of calcium carbonate taken.
Calculation:
Writing the word equation:
Plugging in the values, we get
\begin {split} \text{Calcium carbonate} & = 38 \, \mathrm{g} + 32 \, \mathrm{g} \\ \text {Calcium carbonate} & = 70 \, \mathrm{g}. \end {split}
From this, we can conclude that \(70 \, \mathrm{g}\) of calcium carbonate, on heating, produced \(38 \, \mathrm{g}\) of calcium oxide and \(32 \, \mathrm{g}\) of carbon dioxide respectively.
We now know how to solve theoretical questions related to the law of conservation of mass. Now, let us discuss how to verify the law of conservation of mass experimentally.
Conservation of Mass Experiment
Let's look at an experiment verifying the law of conservation of mass!
Aim of the experiment:
- To verify the law of conservation of mass experimentally.
Chemicals required:
- Lead nitrate(aq) : \(10 \, \mathrm{cm}^3\)
- Potassium iodide : \(10 \, \mathrm{cm}^3\)
Materials required:
- Two \(100 \, \mathrm{cm}^3\) beakers
- A balance
Procedure:
- Take two beakers and fill them with \(10 \, \mathrm{cm}^3\) of aqueous lead nitrate and \(10 \, \mathrm{cm}^3\) of potassium iodide each. Mark the beakers as lead nitrate and potassium iodide (both of them are clear/transparent solutions).
- Measure the mass of the two beakers using a balance. Record the sum of the masses of lead nitrate and potassium iodide as -" Total mass before the reaction."
- Now, carefully pour the aqueous potassium iodide into the beaker containing aqueous lead nitrate. A bright yellow precipitate is formed. Record your observations.
- Now, weigh the beaker with the bright yellow precipitate and record its mass as -"Total mass after the reaction."
Observations:
- A bright yellow precipitate is formed when the contents of the two beakers (lead nitrate and potassium iodide) are mixed, representing a chemical reaction.
- The total mass before and after the reaction is the same.
Fig. 2 - Yellow precipitate of lead iodide.
Inference:
- The law of conservation of mass is verified because the total mass before and after the reaction remained unchanged.
Additional information:
- The reaction between lead nitrate and potassium iodide is a double-displacement chemical reaction. The yellow precipitate is due to the formation of lead iodide.
- The balanced chemical equation is:
\begin {align} 2KI + Pb{(NO_3)}_2 \rightarrow 2KNO_3 + &PbI_2 \\ & (\mathrm{yellow} \\ & \mathrm{precipitate}). \end{align}
Conservation of Mass Equation
The law of conservation of mass is expressed as the following equation in fluid mechanics.
\[ \frac { \partial \rho } { \partial t} + \bigtriangledown ( \rho \, v ) = 0, \]
where
\begin {split} \rho &= \text {density} \\ t& = \text {time} \\ v &= \text{velocity} \\ \bigtriangledown & \, \text{is the divergence}. \end{split}
This equation is also called continuity equation, about which we will learn more in higher studies.
Conservation of Mass - Key takeaways
- Antoine Lavoisier discovered that masses are conserved during a chemical reaction.
- The law of conservation of mass states that in a closed system matter can neither be created nor destroyed, it can only change forms.
- In an open system, if you find an increase in mass at the end of the reaction, it is because one of the reactants is a gas. Likewise, if you notice a decrease in the mass at the end of the reaction, it is because one or two of your products is a gas that has escaped the system.
- An example of conservation of mass: \(2H_2 + O_2 \rightarrow 2H_2O \), where the total number of atoms on either side is 6, while the total relative formula masses on either side are 36.
- Using the law of conservation of mass, we can estimate the unknown amount of a reactant or a product.
- Conservation of mass can be experimentally verified through a simple reaction between lead nitrate and potassium iodide, where a yellow precipitate of lead iodide is formed. On weighing the amounts of chemicals taken before and after the reaction, we will observe that the mass remains unchanged.
References
- Fig. 1 - Portrait of Monsieur Lavoisier and His Wife (https://commons.wikimedia.org/wiki/File:David_-_Portrait_of_Monsieur_Lavoisier_and_His_Wife.jpg) is licensed by Public Domain.
- Fig. 2 - Lead(II) iodide crystals grown in silica gel (https://commons.wikimedia.org/wiki/File:Lead(II)_iodide_crystals_grown_in_silica_gel.JPG#/media/File:Lead(II)_iodide_crystals_grown_in_silica_gel.JPG) by Sjtanarur is licensed by CC BY-SA 4 (https://creativecommons.org/licenses/by-sa/4.0/deed.en).
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