Question

Copper(II) fluoride contains 37.42\(\% \mathrm{F}\) by mass. Calculate the mass of fluorine (in \(\mathrm{g} )\) contained in 55.5 \(\mathrm{g}\) of copper(II) fluoride.

Short answer

The mass of fluorine in 55.5 g of copper(II) fluoride is 20.7781 g.

Step-by-step solution

Identify Percentage of Fluorine in Copper(II) Fluoride

The problem states that copper(II) fluoride contains 37.42% fluorine by mass. This means that in a given mass of copper(II) fluoride, 37.42% of that mass is due to fluorine.

Calculate Mass of Fluorine in Sample

To find the mass of fluorine in the sample, multiply the total mass of copper(II) fluoride by the percentage of fluorine (expressed as a decimal).

Convert Percentage to Decimal

Convert the percentage of fluorine from a percentage to a decimal by dividing by 100: 37.42% / 100 = 0.3742.

Multiply the Sample's Mass by Decimal Percentage of Fluorine

Multiply the mass of the copper(II) fluoride sample by the decimal value of the fluorine percentage to get the mass of the fluorine: 55.5 g * 0.3742 = 20.7781 g of fluorine.

Key concepts

Stoichiometry

Stoichiometry is the backbone of chemical reactions, serving as a quantitative relationship between reactants and products in a chemical equation. It enables chemists to predict the quantities of substances consumed and produced in a given reaction.

For example, using stoichiometry, if you know the amount of one reactant, you can calculate the required amount of another reactant to complete the reaction, or the amount of product that will be formed. This is particularly important in ensuring that reactions are efficient and cost-effective.

In the given exercise, stoichiometry principles are applied in a simpler context where the composition of a compound is used to calculate the mass of a component (fluorine) within the compound. Although no reaction is taking place, understanding the percent composition aligns with stoichiometric concepts, as it involves the proportional parts of each element in a compound.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It is a pivotal concept in stoichiometry for converting between the mass of a substance and the number of moles. To find the molar mass, you add up the atomic masses of all the atoms in a molecule.

In the exercise, calculating the mass of fluorine in copper(II) fluoride doesn't require molar mass directly; however, knowing how to calculate molar mass can help in more complex problems. For instance, if the problem asked for the number of moles of fluorine rather than the mass, you would first find the molar mass of fluorine using the periodic table and then use that to convert the mass to moles.

The molar mass can also be crucial when you want to determine the empirical formula of a compound from its percent composition, as you would need to know how many moles of each element are present.

Empirical Formula

The empirical formula is the simplest ratio of elements in a compound. Unlike the molecular formula, which provides the actual number of atoms of each element in a molecule, the empirical formula is reduced to the lowest whole number ratio.

To determine the empirical formula, you typically start with the percent composition of each element, convert those percentages to masses (if they’re not already given), and then to moles. Once you have the moles, you can find the ratio of the elements to each other.

In our exercise, the problem doesn't require finding the empirical formula, but understanding the concept can enhance the grasp of percent composition. With 37.42% of fluorine in copper(II) fluoride, one could in a different scenario use this percentage to determine the ratio of copper to fluorine atoms and thus, derive the empirical formula of the compound.