Question

A compound of magnesium contains \(21.9 \%\) magnesium, \(27.8 \%\) phosphorus and \(50.3 \%\) oxygen. What will be the simplest formula of the compound? (a) \(\mathrm{Mg}_{2} \mathrm{P}_{2} \mathrm{O}_{7}\) (b) \(\mathrm{MgPO}_{3}\) (c) \(\mathrm{Mg}_{2} \mathrm{P}_{2} \mathrm{O}_{2}\) (d) \(\mathrm{MgP}_{2} \mathrm{O}_{4}\)

Short answer

The simplest formula of the compound is \( \mathrm{Mg}_{2} \mathrm{P}_{2} \mathrm{O}_{7} \) (a).

Step-by-step solution

Assume 100 g of the compound

To make the calculations manageable, assume you have 100 g of the compound. This means you will have 21.9 g of magnesium (Mg), 27.8 g of phosphorus (P), and 50.3 g of oxygen (O).

Convert masses to moles

To find the mole ratio, convert the mass of each element to moles by dividing by the atomic mass. For magnesium: \( \frac{21.9 \text{ g}}{24.305 \text{ g/mol}} \) moles of Mg. For phosphorus: \( \frac{27.8 \text{ g}}{30.974 \text{ g/mol}} \) moles of P. For oxygen: \( \frac{50.3 \text{ g}}{15.999 \text{ g/mol}} \) moles of O.

Determine the smallest number of moles

Divide the number of moles for each element by the smallest number of moles obtained in Step 2. This will yield the simplest whole number ratio of elements in the compound.

Write the empirical formula

Use the mole ratios calculated in Step 3 to write the empirical formula of the compound. If any of the ratios are not whole numbers, multiply all ratios by the smallest number that converts all ratios to whole numbers.

Key concepts

Percent Composition

Understanding the percent composition of a chemical compound is essential when starting to dive into the exciting world of chemistry. Imagine each compound as a tiny universe, with each element representing a part of that universe. The percent composition tells you how much of each element, by mass, is present in the compound.

Take the exercise given, which asks for the simplest formula of a compound with a specific percent composition of magnesium, phosphorus, and oxygen. Starting with the assumption that we have 100 grams of the substance simplifies the calculations – we simply interpret the percentage values as grams directly. This practical step allows us to focus on the proportions of each element, which will lead us to the empirical formula of the compound.

Remember, the key here is to correlate the mass of the elements to the total mass of the compound and express it as a percentage. To take an example from the exercise, 21.9% magnesium means that for every 100 grams of the compound, there are 21.9 grams of magnesium. This concept becomes the cornerstone of the following steps, leading to the calculation of the mole ratio.

Mole Concept

The mole concept is a bridge between the atomic world and everyday measurements. A mole is a unit in chemistry used to represent 6.022 x 10²³ entities, be it atoms, molecules, or particles—this number is known as Avogadro's number. Think of it as a dozen, but instead of 12, it's 6.022 x 10²³.

The reason for converting the mass of elements to moles, as seen in the step-by-step solution, is because it aligns with how elements react on an atomic scale – in fixed proportions by atoms, not by mass. In the given exercise, the formula for converting grams to moles is by dividing the mass of an element by its atomic mass, allowing us to compare the elements on an equal footing – in terms of their atoms.

This calculation results in determining how many moles of each element are present in the sample, which is a crucial step towards identifying the simplest formula. Once we have the moles, we can find a simple whole number ratio among the elements, which leads us to the empirical formula of the compound.

Chemical Formula Determination

Chemical formula determination is like solving a puzzle. It is about finding the simplest whole-number ratio of atoms in a compound, known as the empirical formula. The empirical formula provides the proportions of each type of atom in the compound, but not necessarily the actual numbers of atoms found in the molecule—this is where molecular formulas come in, which can be multiples of the empirical formula.

Following the mole ratios obtained from the mole concept, the smallest mole value is the benchmark. By dividing the moles of each element by this smallest value, we get a simple ratio of atoms. In some cases, these are not whole numbers, and the exercise suggests multiplying these ratios by the smallest number that will convert them into whole numbers, completing the puzzle.

For example, if we get a ratio of half a mole of one element and one mole of another, we multiply by 2 to get whole numbers, ensuring that our chemical formula is based on whole atoms— since you can't have half an atom in a formula. This process distills the essence of the compound into a formula that reflects its actual structure and composition, which in turn helps us understand and predict the behavior of the substance in various chemical reactions.