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 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). The mass ratio is calculated by placing the larger mass on top, resulting in:

Mass Ratio = \(\frac{32 \text{ grams (Oxygen)}}{12.01 \text{ grams (Carbon)}} \approx 2.66\)

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

Understanding this law is crucial for performing calculations related to the composition of compounds. By applying the mass ratios derived from the law of definite proportions, chemists can analyze unknown samples and determine their identity based on their elemental composition. This foundational concept not only aids in chemical analysis but also reinforces the consistency and predictability of chemical compounds in nature.

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:

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:

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.

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.