Law of Definite Proportions: Videos & Practice Problems

The Law of Definite Proportions, also known as Proust's Law or the Law of Constant Composition, states that a chemical compound always contains exactly the same proportion of elements by mass. This foundational chemical principle means that the mass ratios—fractions representing the masses of each element in a compound—remain constant regardless of the sample's source. For example, carbon dioxide (CO₂) from New York City will have the same mass ratio as CO₂ from London, reflecting the consistent mass contributions of carbon (12.1 g/mol) and oxygen (16 g/mol). To determine the mass ratio, the mass of the element with the higher contribution is placed on top. In the case of CO₂, the mass ratio is approximately 2.66, indicating 2.66 grams of oxygen for every gram of carbon. This ratio is crucial for comparing different samples and confirming their identity as the same chemical compound. Understanding and applying this law is essential for analyzing and verifying chemical compositions.

Law of Definite Proportions

The law of definite proportions, also known as Proust's law or the law of constant composition, states that a pure chemical compound always contains the same proportion of elements by mass, regardless of the source of the sample. This principle is fundamental in chemistry, as it allows scientists to determine the composition of compounds based on mass ratios.

To illustrate this concept, consider carbon dioxide (CO₂), which consists of one carbon atom and two oxygen atoms. The atomic mass of carbon is approximately 12.01 grams per mole, while oxygen has an atomic mass of about 16 grams per mole. Therefore, the total mass contributed by carbon in CO₂ is 12.01 grams, and the total mass contributed by oxygen is 32 grams (2 × 16 grams). When calculating the mass ratio, the larger mass (oxygen) is placed on top, resulting in a mass ratio of:

Mass Ratio = \(\frac{32 \text{ grams (O)}}{12.01 \text{ grams (C)}} \approx 2.66\)

This ratio indicates that there are approximately 2.66 grams of oxygen for every gram of carbon in CO₂. According to the law of definite proportions, if two samples of CO₂ were taken from different locations, such as New York City and London, they would yield the same mass ratio of 2.66, confirming that both samples are indeed the same compound.

Understanding the law of definite proportions is crucial for performing calculations related to chemical composition. By applying this law, chemists can compare known samples with unknown ones to determine their identity based on consistent mass ratios. This principle not only reinforces the concept of chemical identity but also serves as a foundation for further explorations in stoichiometry and chemical reactions.

Law of Definite Proportions Example

The law of definite proportions states that a chemical compound always contains its component elements in fixed ratio by mass. This principle can be used to illustrate why nitrogen dioxide (NO₂) and nitric oxide (NO) are distinct compounds by analyzing their mass ratios.

For nitrogen dioxide (NO₂), the composition includes one nitrogen atom and two oxygen atoms. The atomic masses from the periodic table are approximately 14.01 grams per mole for nitrogen and 16.00 grams per mole for oxygen. Therefore, the total mass of oxygen in NO₂ is calculated as:

Mass of O in NO₂ = 2 × 16.00 g/mol = 32.00 g/mol

The mass ratio of oxygen to nitrogen in NO₂ is then:

\[ \text{Mass Ratio}_{NO_2} = \frac{32.00 \, \text{g/mol}}{14.01 \, \text{g/mol}} \approx 2.284 \]

In contrast, nitric oxide (NO) consists of one nitrogen atom and one oxygen atom. Using the same atomic masses, the mass ratio for NO is calculated as follows:

Mass of O in NO = 16.00 g/mol

The mass ratio of oxygen to nitrogen in NO is:

\[ \text{Mass Ratio}_{NO} = \frac{16.00 \, \text{g/mol}}{14.01 \, \text{g/mol}} \approx 1.142 \]

Since the mass ratios of NO₂ and NO are different (2.284 for NO₂ and 1.142 for NO), this difference demonstrates that they are indeed different compounds, as dictated by the law of definite proportions. Each compound has a unique composition that defines its chemical identity.

Law of Definite Proportions Example

Proportions play a crucial role in understanding the law of definite proportions, which states that a chemical compound always contains its component elements in fixed ratio by mass. This principle allows us to determine the unknown mass of an element when the mass ratio and the mass of another element are known.

For instance, consider a substance composed solely of silver and oxygen, where an analysis reveals it contains 3.40 grams of silver and 2.80 grams of oxygen. To find out how many grams of oxygen would be present in a different sample containing 6.63 grams of silver, we can set up a proportion based on the law of definite proportions.

We start by establishing the mass ratios for both samples. The first mass ratio (mass ratio 1) is calculated as:

Mass Ratio 1 = \(\frac{3.40 \, \text{g (Ag)}}{2.80 \, \text{g (O)}}\)

For the second sample (mass ratio 2), we denote the unknown mass of oxygen as \(x\), leading to:

Mass Ratio 2 = \(\frac{6.63 \, \text{g (Ag)}}{x \, \text{g (O)}}\)

According to the law of definite proportions, these two mass ratios are equal:

\(\frac{3.40}{2.80} = \frac{6.63}{x}\)

To solve for \(x\), we cross-multiply:

3.40x = 2.80 × 6.63

Calculating the right side gives:

2.80 × 6.63 = 18.564

Thus, we have:

3.40x = 18.564

Next, we divide both sides by 3.40 to isolate \(x\):

x = \(\frac{18.564}{3.40}\)

Calculating this yields:

x ≈ 5.46 grams

Therefore, in a sample containing 6.63 grams of silver, the corresponding mass of oxygen would be approximately 5.46 grams. This example illustrates how the law of definite proportions can be applied to find unknown quantities in chemical compounds.

The formula for sodium hydroxide is NaOH. A sample of NaOH weighing 18.1124 is found to be comprised of 10.41 g Na and .456 g H. Determine the grams of oxygen most likely to be found in a sample that weighs 25.360 g.

• A. 10.1 g 
• B. 8.29 g
• C. 15.6 g
• D. 16.0 g

Answer: (A)

Here’s what students ask on this topic:

What is the law of definite proportions?

The law of definite proportions, also known as Proust's Law, is a fundamental principle in chemistry that states that a chemical compound always contains exactly the same proportion of elements by mass. This means that no matter the source of a compound or how it was prepared, the ratio of the masses of the elements in the compound will always be the same. For example, water ($H_{2}O$) is composed of hydrogen and oxygen, and it always contains hydrogen and oxygen in a mass ratio of roughly 1:8, respectively. This law is foundational for the understanding of chemical compounds and reactions, as it helps to predict the outcomes of chemical combinations and supports the concept that compounds are composed of fixed ratios of atoms.

Who discovered the law of definite proportions?

The Law of Definite Proportions, also known as Proust's Law, was discovered by the French chemist Joseph Louis Proust. He formulated this fundamental chemical principle between 1797 and 1804. The law states that a chemical compound always contains exactly the same proportion of elements by mass. This means that no matter the source of a chemical compound or how it was prepared, it will always be composed of the same elements in the same proportion by mass. Proust's work was initially controversial but was later confirmed by other scientists and became a cornerstone of modern chemistry, underpinning the stoichiometric principles of compounds.

How does the law of definite proportions apply to compounds?

The law of definite proportions, also known as Proust's Law, states that a chemical compound will always contain the exact same proportion of elements by mass, regardless of the size or source of the compound. For example, water (H2O) is composed of hydrogen and oxygen, and it always contains 2 grams of hydrogen for every 16 grams of oxygen, which gives a fixed mass ratio of 1:8. This means that no matter how much water you have or where you get it from, the proportion of hydrogen to oxygen by mass will remain constant.

In practice, this law means that when compounds are formed, the elements combine in certain fixed ratios and not in any arbitrary amounts. This is a fundamental principle in chemistry that helps chemists understand the composition of substances and predict how they will react with one another. It is also essential for the stoichiometric calculations that are crucial for preparing compounds and for reactions in the lab.