Question

Two different eompounds, each containing only phosphorus and chlorine, were decomposed into their constituent elements. One produced 0.2912 g P for every gram of \(\mathrm{Cl}\); the other produced \(0.1747 \mathrm{~g} \mathrm{P}\) for every gram of Cl. Show that these results are consistent with the law of multiple proportions.

Short answer

The mass ratios of P to Cl are in a 5:3 ratio, confirming the law of multiple proportions.

Step-by-step solution

Understand the Law of Multiple Proportions

The law of multiple proportions states that if two elements form more than one compound, the masses of one element that combine with a fixed mass of the other are in the ratio of small whole numbers. We'll verify this by checking the mass ratios of phosphorus to chlorine.

Calculate the Phosphorus-to-Chlorine Ratio for the First Compound

For the first compound, we have 0.2912 g of phosphorus per 1 g of chlorine. Therefore, the phosphorus-to-chlorine ratio is 0.2912/1.

Calculate the Phosphorus-to-Chlorine Ratio for the Second Compound

For the second compound, we have 0.1747 g of phosphorus per 1 g of chlorine. Therefore, the phosphorus-to-chlorine ratio is 0.1747/1.

Determine the Ratio Between the Two Compounds

To find the ratio of phosphorus masses, divide the ratio from the first compound by the ratio from the second compound: \( \frac{0.2912}{0.1747} \approx 1.666 \), which simplifies to the fraction \( \frac{5}{3} \).

Verify Consistency with the Law of Multiple Proportions

The ratio of \( \frac{5}{3} \) is a simple whole number ratio comparing 5 parts to 3 parts, which satisfies the law of multiple proportions. This demonstrates that the compounds’ formation follows this law.

Key concepts

Phosphorus and Chlorine Compounds

Phosphorus (P) and chlorine (Cl) are elements that can form various compounds through different ways of chemical bonding. These compounds are known for their unique properties and are often studied in chemistry to understand the laws governing chemical reactions.
In our case, we are observing two distinct compounds consisting solely of phosphorus and chlorine. This is an excellent example to apply the law of multiple proportions, which helps chemists discern patterns in how elements combine.
Such phosphorus-chlorine compounds are decomposed to analyze the amount of phosphorus that bonds with a fixed amount of chlorine. These grams of phosphorus per gram of chlorine are key to understanding the chemical nature of these compounds.

Mass Ratios

Mass ratios are quantitative relations between the masses of elements constituting a compound. In the study of these phosphorus and chlorine compounds, it is crucial to determine the mass ratios to apply the law of multiple proportions accurately.
For the first compound, the mass ratio is 0.2912 grams of phosphorus per 1 gram of chlorine, and for the second, it is 0.1747 grams of phosphorus per 1 gram of chlorine.
These ratios allow chemists to compare how much of one element is required to combine with a unit mass of the other, essential to verifying the law of multiple proportions. Calculating these precise ratios is foundational in chemical analysis and helps in making further predictions about the behavior and properties of compounds.

Chemical Decomposition

Chemical decomposition refers to the process of breaking down compounds into their elemental parts. This is often done to study the composition and verify theoretical laws such as the law of multiple proportions.
In this exercise, the compounds of phosphorus and chlorine are decomposed to find out exactly how much phosphorus is involved per unit of chlorine. By doing so, it accentuates the elemental stoichiometry that plays a crucial role in defining chemical compositions.
Understanding decomposition also helps us predict reactions, such as what products form and in what proportions, which is vital for practical chemistry applications.

Whole Number Ratios

The concept of whole number ratios is core to the law of multiple proportions. When the mass ratios of elements forming different compounds are compared, they should simplify to small whole number ratios.
In our example, the calculated ratio between the phosphorus amounts (0.2912 to 0.1747) from each compound results in approximately 1.666, which simplifies to the whole number ratio of 5:3.

• This indicates that for every 5 parts of phosphorus in one compound, there are 3 parts in the other.
• Such simplification is a direct demonstration of the law of multiple proportions, indicating consistent and predictable patterns in elemental composition.

Whole number ratios are crucial in chemical principles, ensuring that compound compositions align with foundational chemical laws.