Question

Two samples of sodium chloride are decomposed into their constituent elements. One sample produces \(4.65 \mathrm{~g}\) of sodium and \(7.16 \mathrm{~g}\) of chlorine, and the other sample produces \(7.45 \mathrm{~g}\) of sodium and \(11.5 \mathrm{~g}\) of chlorine. Are these results consistent with the law of constant composition? Explain your answer.

Short answer

The results are consistent with the law of constant composition because the mass ratio of sodium to chlorine is the same for both samples (\frac{4.65}{7.16} \text{ compared to } \frac{7.45}{11.5}).

Step-by-step solution

Calculate the mass ratio for the first sample

Determine the mass ratio of sodium to chlorine for the first sample by dividing the mass of sodium by the mass of chlorine.

Calculate the mass ratio for the second sample

Calculate the mass ratio for the second sample of sodium chloride in the same manner as in Step 1.

Compare the mass ratios

Compare the mass ratios of sodium to chlorine from both samples. According to the law of constant composition (also known as the law of definite proportions), if the substance is the same, these ratios should be constant, which means they should be approximately the same for both samples.

Conclude if the law of constant composition holds

Based on the comparison, conclude if the results are consistent with the law of constant composition. If the mass ratios are equal, then the law holds true for the given data.

Key concepts

Chemical Decomposition

When studying chemical reactions, one fundamental type of reaction is chemical decomposition. This occurs when a compound breaks down into its constituent elements or simpler compounds.

Imagine baking soda in a cookie recipe; when heated, it decomposes to produce carbon dioxide gas, which in turn helps the cookies rise. Similarly, in the given exercise, sodium chloride (table salt) is decomposed into its elements, sodium and chlorine.

This process is vital to understand because it illustrates how substances are not lost or gained but simply rearranged during chemical reactions. Decomposition is a foundational concept in chemistry that echoes the law of conservation of mass – matter is neither created nor destroyed. Understanding this process is crucial not only for predicting the outcomes of reactions but also for calculating the mass ratios of the resulting elements, which relates directly to the law of definite proportions.

Mass Ratio Calculation

The mass ratio calculation is a technique used to express the proportion of elements in a compound. It involves dividing the mass of one element by the mass of another.

In the context of the given exercise, the mass ratio for sodium to chlorine is calculated by dividing the mass of sodium by the mass of chlorine for each sample. For the first sample, this means dividing 4.65 g of sodium by 7.16 g of chlorine.

Calculating Mass Ratios:

For the first sample: \(\frac{4.65~\text{g Na}}{7.16~\text{g Cl}} \)For the second sample: \(\frac{7.45~\text{g Na}}{11.5~\text{g Cl}} \)The calculated ratios provide an insight into the composition of the compound and serve as a comparison point to verify scientific laws like the law of constant composition.

Law of Definite Proportions

The law of definite proportions, also known as the law of constant composition, states that a chemical compound will always be composed of the same elements in the same proportions by mass, regardless of the size of the sample or the source of the compound.

This means that if you have two samples of pure sodium chloride, the mass ratio of sodium to chlorine will be consistent between the samples.

Applying the Law to Exercise Results:

By comparing the mass ratios calculated in the exercise, we can assess if they are consistent. For the law to hold true, the mass ratios should be approximately equal. If they are indeed equal or nearly so, we can conclude that the results are aligned with the law of definite proportions–a fundamental principle guiding the composition of compounds in chemistry.