Law of Definite Proportions: Videos & Practice Problems

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 and who discovered it?

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, regardless of the sample's source. This means that any pure sample of a compound will have the same mass ratio of its constituent elements. The law was discovered by the French chemist Joseph L. Proust in 1799. It is fundamental in chemistry because it helps confirm the identity of compounds by comparing their mass ratios. For example, carbon dioxide (CO₂) from different locations will have the same mass ratio of oxygen to carbon, demonstrating the law's consistency.

How do you calculate the mass ratio of elements in a compound according to the Law of Definite Proportions?

To calculate the mass ratio of elements in a compound, first determine the atomic masses of each element from the periodic table. Then multiply the atomic mass by the number of atoms of that element in the compound. For example, in carbon dioxide (CO₂), carbon has an atomic mass of 12.01 g/mol and oxygen has 16.00 g/mol. Since there are two oxygen atoms, multiply 16.00 by 2 to get 32.00 g. The mass ratio is then calculated by placing the larger mass on top and dividing by the smaller mass: $\frac{32.00}{12.01}$ ≈ 2.66. This means there are approximately 2.66 grams of oxygen for every gram of carbon in CO₂.

Why is the Law of Definite Proportions important in identifying chemical compounds?

The Law of Definite Proportions is important because it ensures that a pure chemical compound has a consistent and fixed mass ratio of its elements. This consistency allows chemists to identify and verify compounds by comparing the mass ratios of unknown samples to known standards. For example, if two samples suspected to be carbon dioxide have the same oxygen-to-carbon mass ratio of about 2.66, they are likely the same compound. If the ratios differ, the samples are not the same compound. This law is fundamental in analytical chemistry and helps maintain accuracy in chemical composition analysis.

Can the Law of Definite Proportions be used to compare samples of the same compound from different locations?

Yes, the Law of Definite Proportions states that any pure sample of a chemical compound, regardless of its source or location, will have the same fixed mass ratio of its constituent elements. For example, carbon dioxide (CO₂) collected from New York City and London will have the same mass ratio of oxygen to carbon, approximately 2.66. This consistency allows chemists to confirm that samples from different locations are chemically identical by comparing their mass ratios, which is a practical application of the law.

What is the difference between the Law of Definite Proportions and the Law of Multiple Proportions?

The Law of Definite Proportions states that a chemical compound always contains the same elements in the same fixed mass ratio, regardless of the sample size or source. In contrast, the Law of Multiple Proportions applies when two elements form more than one compound; it states that the masses of one element that combine with a fixed mass of the other are in ratios of small whole numbers. Essentially, the Law of Definite Proportions deals with the composition of a single compound, while the Law of Multiple Proportions explains the relationship between different compounds made from the same elements.