Law of Definite Proportions: Videos & Practice Problems

The law of definite proportions, also known as Proust's law, states that a pure chemical compound always contains the same mass ratios of its constituent elements. For example, carbon dioxide (CO₂) consists of 1 carbon atom and 2 oxygen atoms, with respective atomic masses of 12.01 g/mol and 16 g/mol. The mass ratio of oxygen to carbon is approximately 2.66, indicating that in any sample of CO₂, this ratio remains constant. This principle is crucial for identifying and comparing chemical compounds across different samples.

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, in a molecule of CO₂, the total mass contributed by carbon 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 is placed on top. In this case, the mass ratio of oxygen to carbon is calculated as follows:

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

This result 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 and for identifying unknown samples based on their mass ratios. This law serves as a foundational concept in stoichiometry, which is the study of the quantitative relationships in chemical reactions.

Law of Definite Proportions Example 1

In this scenario, we are examining two unknown compounds, A and B, to determine if they represent the same chemical substance based on the law of definite proportions. This law states that a chemical compound always contains its component elements in fixed ratio by mass. To analyze this, we need to calculate the mass ratios of hydrogen to oxygen for both compounds.

For compound A, we have:

Mass of hydrogen = 2 grams

Mass of oxygen = 32 grams

The mass ratio of oxygen to hydrogen for compound A is calculated as:

Mass Ratio A = \(\frac{32 \text{ grams O}}{2 \text{ grams H}} = 16\)

For compound B, the values are:

Mass of hydrogen = 15 grams

Mass of oxygen = 120 grams

The mass ratio of oxygen to hydrogen for compound B is:

Mass Ratio B = \(\frac{120 \text{ grams O}}{15 \text{ grams H}} = 8\)

These calculations reveal that compound A has a mass ratio of 16:1 (16 grams of oxygen for every 1 gram of hydrogen), while compound B has a mass ratio of 8:1 (8 grams of oxygen for every 1 gram of hydrogen). Since the mass ratios of the two compounds are not equal, we conclude that compounds A and B do not represent the same compound.

In summary, the differing mass ratios indicate that the two samples are distinct substances, demonstrating the application of the law of definite proportions in chemical analysis.

Law of Definite Proportions Example 2

Understanding mass ratios and proportions is essential for determining whether different samples represent the same compound. This concept is particularly useful when applying the law of definite proportions, which states that a chemical compound always contains its component elements in fixed mass ratios.

For instance, consider a compound composed solely of calcium and fluorine. If a sample contains 2 grams of calcium and 1.90 grams of fluorine, we can establish a mass ratio. According to the law of definite proportions, this ratio must remain constant across different samples of the same compound.

To find out how much calcium should be present in another sample containing 2.85 grams of fluorine, we set up a proportion based on the known mass ratio. The initial mass ratio (mass ratio a) is:

\[ \text{Mass Ratio a} = \frac{2 \text{ g Ca}}{1.90 \text{ g F}} \]

For the second sample (mass ratio b), we have:

\[ \text{Mass Ratio b} = \frac{x \text{ g Ca}}{2.85 \text{ g F}} \]

Since both ratios must be equal, we can write:

\[ \frac{2}{1.90} = \frac{x}{2.85} \]

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

\[ 1.90x = 2 \times 2.85 \]

Calculating the right side gives:

\[ 1.90x = 5.70 \]

Next, we isolate \(x\) by dividing both sides by 1.90:

\[ x = \frac{5.70}{1.90} \approx 3.00 \text{ g Ca} \]

This calculation shows that if the second sample contains 2.85 grams of fluorine, it should contain approximately 3.00 grams of calcium. By utilizing mass ratios and proportions, we can effectively determine the composition of compounds and verify if different samples represent the same chemical entity.

A 7.74 g sample of HCN is found to contain 0.287 g of H and 4.01 g N. Find the mass of carbon in a sample of HCN with a mass of 3.43 g.

• A. 1.28 g C
• B. 1.53 g C
• C. 1.70 g C
• D. 2.01 g C

Answer: (B)

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, states that a pure chemical compound always contains the same mass ratios of its constituent elements. For example, in carbon dioxide (CO₂), the mass ratio of oxygen to carbon is approximately 2.66. This means that in any sample of CO₂, the ratio of the mass of oxygen to the mass of carbon will always be the same, regardless of the sample's origin. This principle is crucial for identifying and comparing chemical compounds across different samples.

How do you calculate the mass ratio in the law of definite proportions?

To calculate the mass ratio in the law of definite proportions, you need the atomic masses of the elements involved. For example, in CO₂, carbon has an atomic mass of 12.01 g/mol and oxygen has an atomic mass of 16 g/mol. Since CO₂ has one carbon atom and two oxygen atoms, the total mass of carbon is 12.01 g and the total mass of oxygen is 32 g (16 g/mol × 2). The mass ratio is calculated by dividing the larger mass by the smaller mass: $\frac{32}{12.01}$ ≈ 2.66. This ratio indicates that there are approximately 2.66 grams of oxygen for every gram of carbon in CO₂.

Why is the law of definite proportions important in chemistry?

The law of definite proportions is important in chemistry because it ensures the consistency and predictability of chemical compounds. By knowing that a compound always contains the same elements in the same proportions by mass, chemists can identify and verify the purity of substances. This law also helps in understanding chemical reactions and stoichiometry, as it provides a foundation for calculating the amounts of reactants and products involved in chemical processes.

Can the law of definite proportions be used to identify unknown compounds?

Yes, the law of definite proportions can be used to identify unknown compounds. By determining the mass ratios of the elements in an unknown sample and comparing them to the known mass ratios of potential compounds, chemists can identify the compound. For example, if an unknown sample has a mass ratio of oxygen to carbon of approximately 2.66, it is likely to be CO₂. This method is particularly useful in analytical chemistry for verifying the composition of substances.

What is an example of the law of definite proportions in everyday life?

An example of the law of definite proportions in everyday life is table salt (sodium chloride, NaCl). Regardless of where the salt is sourced from—whether it is from a salt mine, seawater, or produced in a laboratory—the mass ratio of sodium to chlorine in NaCl is always the same. Sodium has an atomic mass of approximately 23 g/mol, and chlorine has an atomic mass of approximately 35.5 g/mol. The mass ratio of chlorine to sodium in NaCl is $\frac{35.5}{23}$ ≈ 1.54, meaning there are 1.54 grams of chlorine for every gram of sodium.