Question

Two samples of sodium chloride are decomposed into their constituent clements. One sumple produces 6.98 of sodium and 10.77 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.

Short answer

The results are consistent with the law of definite proportions if the mass ratio of chlorine to sodium is the same in both samples.

Step-by-step solution

Calculate the mass ratios of chlorine to sodium for both samples

To verify the law of definite proportions, calculate the mass ratio of chlorine to sodium for both samples. For the first sample, divide the mass of chlorine (10.77 g) by the mass of sodium (6.98 g) to get the ratio. For the second sample, divide the mass of chlorine (17.3 g) by the mass of sodium (11.2 g) to find its ratio.

Compare the ratios

Compare the two mass ratios calculated in the previous step. The law of definite proportions states that a chemical compound will always contain the same proportion of elements by mass, regardless of the quantity or source of the compound. If the ratios are the same or very close to being the same within experimental error, then the results are consistent with the law of definite proportions.

Conclusion based on comparison

Determine if the mass ratios from both samples are consistent with the law of definite proportions. If they are the same or very close, the law is confirmed; if not, it suggests a violation of the law.

Key concepts

Understanding Chemical Compound Composition

The world of chemistry is fascinating, with its intricate dance of atoms combining to form substances with unique properties. This is encapsulated in chemical compound composition, which is central to our exploration of the law of definite proportions. For instance, table salt, or sodium chloride, is always composed of sodium (Na) and chlorine (Cl) in a fixed ratio by mass.

A chemical compound such as sodium chloride has a specific recipe – you might think of it like a baker's recipe for a signature bread – that never changes. If it did, we wouldn’t end up with the familiar substance we know. This constancy is essential for the compound's consistency and behavior. This is why, when samples of sodium chloride are decomposed into their elements, as in our exercise, if they adhere to the law of definite proportions, they should always yield sodium and chlorine in the same fixed ratio by mass, regardless of the size of the sample or its source.

Mass Ratio Calculation

Let's demystify the concept of mass ratio calculation. In our exercise involving sodium chloride, we're like detectives checking if our two samples come from the same 'culinary recipe.' By dividing the mass of chlorine by the mass of sodium for each sample, we're able to determine the mass ratio of chlorine to sodium.

The step-by-step process outlined in the solution section helps to illustrate this calculation. When we take the mass of chlorine (10.77 g) and divide it by the mass of sodium (6.98 g) for the first sample, we obtain a precise ratio. We repeat this with the second sample's 17.3 g of chlorine and 11.2 g of sodium. The comparison of these ratios tells us if the composition of the two samples is indeed uniform as the law suggests. This comparison is critical in confirming that a compound's mass composition is definitive and reproducible, a cornerstone concept in chemical studies.

The Principle of Stoichiometry

Moving to stoichiometry, this is the branch of chemistry that deals with the quantitative relationships between the reactants and products in chemical reactions. The law of definite proportions ties directly into stoichiometry as it ensures that the proportions of elements in compounds are constant and can be predicted.

In stoichiometry, scientists use the law as a foundation to calculate how much of a reactant is needed to create a desired amount of product, or vice versa. From the mass ratios calculated previously, stoichiometry helps to delve deeper into the quantitative aspects of our sodium chloride samples. In practical terms, it assures us that if we understand the composition of a compound, we can scale its production up or down, while expecting the same outcome – much like multiplying a recipe to serve a larger crowd or reducing it for a cozy dinner for two. It's this precision and predictability that makes stoichiometry so powerful in the fields of chemistry and chemical engineering.