# Law of Definite Proportions

If you bought a standard deck of 52 cards, how many cards of each of the four suits of diamonds, hearts, clubs, and spades are you expecting to have in the deck? Well, each suit always has 13 cards, Ace through King!  No matter what store you bought the cards from, the material the cards are made out of, or anything else, the ratio of cards in the deck is always the same! This same concept applies to the elemental composition of a pure compound in what we will learn is called the law of definite proportion.

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• In this introduction, we are going to define the law of definite proportions clearly
• Then, we will look at the law of definite proportions formula
• Next, we will go back in time to explore the experiment that led to the law of definite proportions
• We will spend some time looking at examples of applying this law
• Finally, we will differentiate between the law of definite proportions and the law of multiple proportions

If you aren't familiar with the composition of matter or haven't read Elemental Composition of a Pure Substance yet, review those topics and come back!

## Law of Definite Proportions Definition

Let's break down what the law of definite proportions definition actually means!

The law of definite proportion states that the elemental composition of pure compounds is a fixed ratio of elements by mass.

We are going to look at all the bolded aspects of the law of definite proportion definition:

• Remember, compounds are a class of matter known as pure substances, so the elemental composition of compounds is bonded atoms from two or more elements
• according to this law, every sample of a particular compound has a fixed ratio of elements meaning the same elements in the same proportions by mass
• We are looking at the ratio of elements to compounds according to their molecular weights, which is the percent composition.

Another way to say that compounds have a fixed ratio of compounds by mass is to say that they always have the same percent composition. This is because percent composition refers to the relative mass of each element in a compound! We introduced percent composition in Elemental Composition of a Pure Substance, so check it out for a refresher!

The implication of the law of definite proportion is that no matter the source of the elements or the amount of the compound, the ratio of elements must be constant to form the compound.

Based on what we have covered so far, if we take 10 L of water from a lake and 5 L of water from a river, will the ratio of hydrogen to oxygen in the 10 L sample be larger? Why or why not? Please take a second to think of your answer before we think through it together!

The correct answer is: No, the ratio will not be larger in the 10 L sample. The law of definite proportions tells us that water will always have the same ratio of elements. Both water samples are composed of 2 hydrogen atoms and 1 oxygen atom. Water molecules are 11 % hydrogen and 88 % oxygen by mass. So, the 10 L sample and 5 L sample of the water will have the same ratio of elements!

Fig.1-According to the law of definite proportions, pure water (H2O) from any source has the same percentage composition of Hydrogen and Oxygen.

## Law of Definite Proportions Formula

Now that we are familiar with the conceptual side of the law of definite proportions let's take a look at a formula that shows the relationship between compounds and fixed ratios!

An easy way to represent the law of definite proportions is through the percent composition formula :\begin {align}\%\,Composition\,of\,AB &= \\\%\,of\,A &= \frac{mass\,of\,element\,A*atoms\,of\,element\,A}{total\,molecular\,mass\,of\,AB}*100\% \\\%\,of\,B &= \frac{mass\,of\,element\,B*atoms\,of\,element\,B}{total\,molecular\,mass\,of\,AB}*100\% \\\end {align}

Next, we will do a couple of examples applying the law of definite proportion and determine the percent composition of various compounds!

## Law of Definite Proportions Examples

A broad example of the law of definite proportions would be Glucose (C6H12O6). Glucose is always made up of 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms. This is the only ratio of these three elements that can make glucose.

Keeping this in mind, we will go over a thorough example of applying the law of definite proportion by calculating the percent composition of glucose together.

One type of question that's important to know how to answer is the following:

Find the percent composition of all elements in the glucose (C6H12O6).

1) First, we need to break down one molecule of glucose into the correct elements

• 6 carbon atoms
• 12 hydrogen atoms
• 6 oxygen atoms

2)Then, we look at the period table to determine the relative atomic mass of these elements and multiply it by the number of atoms of each element

• C : $$6\,atoms*12.011\frac{g}{mol}=72.066\,g$$
• H : $$12\,atoms*1.008\frac{g}{mol}=12.096\,g$$
• O : $$6\,atoms*15.999\frac{g}{mol}=95.994\,g$$

4) Then, we find the total weight of glucose:

$$72.066\,g+12.011\,g+95.994\,g=180.156\,g$$

5) Finally, we calculate the mass percent of each element using our equation:

$$mass\%=\,(\frac{mass\,of\,component}{mass\,of\,total})*100\%$$

• Mass % of C = $$(\frac{72.066\,g}{180.156\,g})*100\%=40.001\%$$

• Mass % of H = $$(\frac{12.096\,g}{180.156\,g})*100\%=6.714\%$$

• Mass % of O = (\frac{95.994\,g}{180.156\,g})*100\%=53.284\%

Here is a different type of question applying the law of definite proportions!

If the percent composition of carbon in CO2 is 29.27%, what is the percent composition of oxygen?

There is a straightforward way to solve this! The percent composition of all the elements must add up to 100%. So, we can subtract 29.27 from 100, which means the percent mass of oxygen is 72.71%.

Here are some tips for calculating percent mass:

• always pay attention to what exactly the question is asking for (percent mass, mass in g, etc.)
• all your percentages at the end should always add up to 100%

## Law of Definite Proportions Experiment

Maybe you think that the law of definite proportion seems pretty straightforward. Of course, a compound would have to be made up of the same ratio of elements every time! But, just like the law of gravity wasn't always obvious, the concept of definite proportions in compounds was once unknown!

In the early 1800s, a chemist named Joseph Proust experimented with copper carbonate (CH₂Cu₂O₅). Proust synthesized artificial copper carbonate and compared this lab product to naturally occurring copper carbonate. After analyzing both substances, Provost found that both samples of copper carbonate contained the same weight proportions of the three elements involved: carbon, oxygen and copper. In Proust's own words, the experiment showed that

A chemical compound always contains the same elements combined together in the same proportion by mass. - Joseph Proust

Thus, the law of definite proportions was born!

## Law of Definite Proportions vs. Law of Multiple Proportions

Even though Proust published his law around 1794, it wasn't until chemist John Dalton published his atomic theory and his law of multiple proportions around 1804 that the law of definite proportions became widely accepted.

Dalton's law of multiple proportions states that when two elements can combine to form a multitude of different compounds, one element with a fixed mass combines with different masses of the second element, whose mass ratio can be expressed as a ratio of small, whole numbers.

The law of multiple proportions would explain compounds such as:

• NO, NO2
• CO, CO2
• CH2, CH4

These compounds are made up of the same elements, but have different ratios of the second element in the two compounds.

Fig.2-NO and NO2 proportions

Let's look at an example to understand the application of multiple proportions law better.

Looking at NO and NO2, we can see this law played out.

The mass of nitrogen in both compounds remains fixed at 14 g

The mass of oxygen in NO = 16 grams

The mass of oxygen in NO2 = 32 grams

The mass ratio between O in NO and NO2 is 32:16, which can be simplified to 1:2!

You may notice that the 1:2 ratio of O in NO and NO2 is represented by molecular formulas! It's important to realize that molecular formulas were not known when Dalton published the Law of Multiple Proportions. Chemists knew that when different masses of oxygen bonded with a fixed mass of carbon, different compounds with different properties would form! So, this law was one thing that paved the way for molecular formulas!

## Law of Definite Proportions - Key takeaways

• The law of definite proportions states that the elemental composition of pure compounds is a fixed ratio of elements by mass. Joseph Proust is credited with publishing the law.
• The implications of this law mean that regardless of the source or amount of a compound, the mass ratio of the elements in the compound is the same.
• the mass ratio of the element in a compound is known as percent composition
• The formula related to the Law of Definite Proportions is, % mass = (mass of element/mass of compound) x100
• The Law of Multiple Proportions explains that the relationship of mass ratios of elements that can form two different compounds will be small, whole numbers.

#### Flashcards in Law of Definite Proportions 14

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What is law of definite proportions?

The law of proportions explains the fixed elemental composition of compounds. It states that the elemental composition of pure compounds is a fixed ratio of elements by mass.

Who discovered the law of definite proportions?

The law of definite proportions was discovered in 1794 by a French chemist named Joseph Proust. He conducted experiments with artificial and natural copper carbonate.

What is the law of definite and multiple proportions?

The law of definite and multiple proportions are two different laws related to the composition of elements. The law of definite proportions explains that compounds have fixed ratios of elements. The law of multiple proportions expands this concept to explain that the mass ratio of the same elements in different compounds can be represented by small, whole numbers.

What is the law of definite proportion with examples?

The law of definite proportion means that compounds have a fixed mass ratio of elements. An example of this would be water from different bodies of water will still be made up of 11% hydrogen and 89% oxygen.

How to solve law of definite proportions?

To solve the law of definite proportions in a mathematical sense, the percent mass composition of elements in a compound is calculated.  The individual masses of the elements are found on the periodic table and multiplied by the number of atoms in the molecule if applicable. Then, that number is divided by the total weight of the compound and multiplied by 100. The percent mass formula is (mass of element*# of atoms/mass of compound) x100.

## Test your knowledge with multiple choice flashcards

True or False. The law of definite proportions implies that the source of the compound does not affect the fixed mass ratio of elements but the amount of the compound does.

What is true of the law of definite proportions?

Select the statements below where the law of definite proportions is correctly applied.

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