Problem 31 - Chemistry A Molecular Approach

Question

Two samples of sodium chloride are decomposed into their constituent elements. One sample produces \(6.98 \mathrm{~g}\) of sodium and \(10.7 \mathrm{~g}\) of chlorine, and the other sample produces \(11.2 \mathrm{~g}\) of sodium and \(17.3 \mathrm{~g}\) of chlorine. Are these results consistent with the law of definite proportions? Explain your answer.

Step-by-Step Solution

Answer

Mass ratio for Sample 1 = 1.5344 g/g, and for Sample 2 = 1.5446 g/g. Since the ratios are very close, the results are consistent with the law of definite proportions.

Step 1: Calculate the Mass Ratios

To determine if the law of definite proportions holds, you need to calculate the mass ratio of chlorine to sodium for both samples. For the first sample, the mass ratio is calculated by dividing the mass of chlorine by the mass of sodium. Use the formula: mass ratio of Sample 1 = mass of chlorine / mass of sodium. Perform the calculation: mass ratio of Sample 1 = 10.7 g / 6.98 g.

Step 2: Repeat the Calculation for the Second Sample

Calculate the same mass ratio for the second sample of sodium chloride using the analogous formula: mass ratio of Sample 2 = mass of chlorine / mass of sodium. Now perform the calculation: mass ratio of Sample 2 = 17.3 g / 11.2 g.

Step 3: Analyze the Results

Compare the mass ratios obtained in the previous steps. If the ratios are the same (or very close allowing for experimental error), this supports the law of definite proportions, which states that a chemical compound always contains exactly the same proportion of elements by mass. Calculate and compare the decimal mass ratios to determine if they are consistent.

Key Concepts

Mass Ratio in Chemistry

The concept of mass ratio is fundamental to understanding chemical reactions. It refers to the ratio of the masses of substances involved in the reaction. Specifically, in the context of a compound like sodium chloride (NaCl), the mass ratio is the weight of chlorine divided by the weight of sodium in a given sample.

This ratio is essential because it demonstrates the law of definite proportions, which posits that a chemical compound will always be composed of the same elements in the same proportion by mass, regardless of the size or source of the sample. For example, if two different samples of NaCl are broken down into sodium and chlorine, the mass ratios of chlorine to sodium should be the same for both samples, assuming there are no experimental errors. It is this consistency that was tested in the original exercise by comparing the mass ratios from two disparate samples.

Chemical Compound Composition

Understanding the composition of a chemical compound is crucial in chemistry. Each compound has a unique formula that specifies the types and numbers of atoms present. In the case of sodium chloride, for every atom of sodium, there is one atom of chlorine. This 1:1 ratio remains constant, which is an example of the law of definite proportions at the atomic level.

The composition of compounds is not only described in terms of atoms but also in terms of mass, as seen in the exercise. When you break down a compound, the mass of each element derived from it is not arbitrary but is an intrinsic property of the compound. This concept of composition is intertwined with the mass ratio, as changes in composition logically affect the mass ratio of the elements that make up the compound.

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantification of reactants and products in a chemical reaction. It allows chemists to predict the amounts of products that will form in a given reaction or the amounts of reactants needed to create a certain amount of product. The stoichiometric coefficients indicate the ratios of reactants and products involved in the reaction.

For instance, when decomposing sodium chloride, stoichiometry tells us that one mole of NaCl will produce one mole of sodium and one mole of chlorine gas, based on the balanced chemical equation. This mole ratio translates to a fixed mass ratio because each element has a specific molar mass, which is another way to express the law of definite proportions. When there's a deviation from the stoichiometric ratios, it raises a question about the purity of the reactants or the occurrence of experimental errors.

Experimental Error in Chemistry

Experimental error is a natural part of any scientific investigation, encompassing all the uncertainties and deviations that can occur when measuring, sampling, or experimenting. These errors can be systematic, resulting from flawed equipment or procedures, or random, as a result of unpredictable variations in observations.

In our exercise, if the mass ratios of chlorine to sodium from two samples of sodium chloride differ, it might initially suggest a contradiction to the law of definite proportions. However, it's important to consider experimental error as a possible explanation for any discrepancy. Small variations in measurements are expected, and only significant differences would challenge the law. Accurate analytical techniques are crucial to minimize these errors and confirm the consistency required by chemical laws.