Problem 14 - General Chemistry: Principles and Modern Applications

Question

Phosphorus forms two compounds with chlorine. In the first compound, \(1.000 \mathrm{g}\) of phosphorus is combined with \(3.433 \mathrm{g}\) chlorine, and in the second, \(2.500 \mathrm{g}\) phosphorus is combined with \(14.308 \mathrm{g}\) chlorine. Show that these results are consistent with Dalton's law of multiple proportions.

Step-by-Step Solution

Answer

The ratios of the masses of chlorine that combine with a fixed mass of phosphorus in the two compounds are approximately 5/3. This is a simple whole number ratio, thus proving these results to be consistent with Dalton's law of multiple proportions.

Step 1: Identify given data

Identify and list the given data. The mass of phosphorus and chlorine in the first compound is 1.000 g and 3.433 g respectively. For the second compound, the masses are 2.500 g and 14.308 g respectively.

Step 2: Calculate the mass ratios

Calculate the ratios of the masses of chlorine that combine with a fixed mass of phosphorus for both compounds. For the first compound, it's \(\frac{3.433g}{1.000g} = 3.433\). For the second compound, it's \(\frac{14.308g}{2.500g} = 5.7232\). These are not simple whole numbers but they might be in lowest terms.

Step 3: Simplify the ratios

To check if these ratios simplify to whole numbers, calculate the ratio of the two previous ratios. That is, \(\frac{5.7232}{3.433} = 1.667 ≈ 5/3\). Thus, we can conclude that the ratios are indeed whole numbers when in lowest terms, confirming Dalton's law.

Key Concepts

Phosphorus and Chlorine Compounds

Phosphorus and chlorine are two elements that can combine to form various compounds, relying on the proportions of each element. In our example, phosphorus combines with chlorine to form two distinct compounds.

• In the first compound, a fixed mass of phosphorus (1.000 g) is combined with 3.433 g of chlorine.
• In the second compound, 2.500 g of phosphorus is used and combines with 14.308 g of chlorine.

The key point to notice here is how each compound has a different ratio of chlorine to phosphorus. These compounds illustrate a fundamental concept in chemistry, specifically Dalton's law of multiple proportions. This law allows chemists to deduce that there can be different ratios that involve the same elements forming different compounds.

Mass Ratios

The concept of mass ratios involves comparing the mass of one element to another within a compound. This is essential when applying Dalton's law of multiple proportions.

• In the first compound, the mass ratio of chlorine to phosphorus is \( \frac{3.433}{1.000} = 3.433 \).
• For the second compound, the mass ratio becomes \( \frac{14.308}{2.500} = 5.7232 \).

The mass ratios give insight into how different amounts of chlorine can pair up with a fixed proportion of phosphorus to create unique substances. Although these numbers aren't initially simple whole numbers, they can be analyzed further. By getting the ratio of these ratios \( \frac{5.7232}{3.433} = 1.667 \approx \frac{5}{3} \), we find a simple ratio indicating the law in question: a clear demonstration of simple whole number ratios as anticipated by Dalton's theory.

Chemical Laws

Chemical laws provide a foundation for understanding reactions and compound formations. Dalton's law of multiple proportions is one of these key laws explaining how elements form different compounds.This law states that when two elements form multiple compounds, the masses of one element that combine with a fixed mass of the other are in simple whole number ratios. By applying this to our phosphorus and chlorine compounds:

• The simplified ratio of mass ratios \( \frac{5.7232}{3.433} \approx \frac{5}{3} \) shows a simple relationship.
• Thus, confirming that different compounds formed by these elements follow Dalton's principle.

Dalton's law helps predict the possibility of forming distinct compounds from the same elements, based on these whole-number mass ratios. This fundamental principle aids in comprehending the diverse ways elements can interact to build the array of chemical substances observed in nature.