Question

Although we usually think of substances as "burning" only in oxygen gas, the process of rapid oxidation to produce a flame may also take place in other strongly oxidiring gases. For cxample, when iron is heated and placed in pure chlorine gas, the iron "burns" according to the following (unbalanced) reaction: $$ \mathrm{Fe}(s)+\mathrm{Cl}_{2}(g) \rightarrow \mathrm{FeCl}_{3}(s) $$ How many milligrams of iron(III) chloride result when \(15.5 \mathrm{mg}\) of iron is reacted with an excess of chlorine gas?

Short answer

When 15.5 mg of iron reacts with an excess of chlorine gas, 44.9 mg of iron(III) chloride is produced.

Step-by-step solution

Balance the reaction

First, we need to balance the reaction: \(2 \mathrm{Fe}(s) + 3\mathrm{Cl}_{2}(g) \rightarrow 2\mathrm{FeCl}_{3}(s)\) The balanced reaction is as follows: \(2 \mathrm{Fe}(s) + 3\mathrm{Cl}_{2}(g) \rightarrow 2\mathrm{FeCl}_{3}(s)\)

Convert mass of iron to moles

Next, we need to convert the given mass of iron (15.5 mg) to moles. The molar mass of iron is 55.85 g/mol. Since we have the mass in milligrams, it's a good idea to convert it to grams first: \(15.5\,\mathrm{mg} \times \frac{1\,\mathrm{g}}{1000\,\mathrm{mg}} = 0.0155\,\mathrm{g}\) Now we can convert the grams of iron to moles: \(\frac{0.0155\,\mathrm{g}}{55.85\,\mathrm{g/mol}} = 2.77 \times 10^{-4}\,\mathrm{mol}\)

Determine the stoichiometric ratio

From the balanced reaction, the stoichiometric ratio between iron and iron(III) chloride is 2:2 or 1:1. This means that 1 mole of iron will produce 1 mole of iron(III) chloride.

Calculate moles of iron(III) chloride produced

Since the stoichiometric ratio is 1:1, the moles of iron(III) chloride produced will be the same as the moles of iron reacted: \(2.77 \times 10^{-4}\,\mathrm{mol\,Fe} \times \frac{1\,\mathrm{mol\,FeCl}_{3}}{1\,\mathrm{mol\,Fe}} = 2.77 \times 10^{-4}\,\mathrm{mol\,FeCl}_{3}\)

Convert moles of iron(III) chloride to milligrams

Finally, we need to convert the moles of iron(III) chloride produced back into milligrams. The molar mass of iron(III) chloride is 162.2 g/mol. First, we'll convert moles to grams: \(2.77 \times 10^{-4}\,\mathrm{mol\,FeCl}_{3} \times \frac{162.2\,\mathrm{g}}{1\,\mathrm{mol\,FeCl}_{3}} = 0.0449\,\mathrm{g}\) Now, convert grams to milligrams: \(0.0449\,\mathrm{g} \times \frac{1000\,\mathrm{mg}}{1\,\mathrm{g}} = 44.9\,\mathrm{mg}\) Therefore, when 15.5 mg of iron reacts with an excess of chlorine gas, 44.9 mg of iron(III) chloride is produced.

Key concepts

Stoichiometry

Stoichiometry is a vital concept in chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. Imagine baking cookies; stoichiometry helps you decide how much flour and sugar you need based on how many cookies you want to make. In a chemical reaction, stoichiometry allows us to predict the amount of product formed from given quantities of reactants.
For instance, in the reaction between iron and chlorine gas to form iron(III) chloride, stoichiometry is used to determine the exact amount of each substance that will react and the amount of product that will result. This is crucial for optimizing chemical processes in labs or industries, ensuring minimal waste and maximum efficiency.

Oxidation

Oxidation is a process involving the loss of electrons from an element. It is a part of many chemical reactions, especially those that involve burning or rusting. In the oxidation process, elements react with oxygen or other electronegative elements.
In our example reaction, iron (which is the substance being oxidized) reacts with chlorine gas, a strongly oxidizing agent. Here, iron loses electrons to chlorine, forming iron(III) chloride. This transfer of electrons is what chemically binds iron and chlorine together. Understanding oxidation is essential for students and researchers because it helps explain how different substances interact and transform during chemical reactions.

Balancing Chemical Equations

Balancing chemical equations is like balancing a set of scales. Each side needs to have the same amount of mass and atoms to truly reflect the law of conservation of mass. Initially, the equation for the reaction between iron and chlorine gas might say \(\mathrm{Fe}(s) + \mathrm{Cl}_{2}(g) \rightarrow \mathrm{FeCl}_{3}(s)\). This is unbalanced because the number of atoms on each side isn't equal.
By balancing the equation, we change it to \(2 \mathrm{Fe}(s) + 3\mathrm{Cl}_{2}(g) \rightarrow 2\mathrm{FeCl}_{3}(s)\). This balanced version ensures that there are equal amounts of iron and chlorine atoms on both sides of the equation. Balancing is crucial because it reflects the true nature of reactants and products during a chemical reaction, ensuring accuracy in stoichiometric calculations.

Molar Mass Calculation

Molar mass calculation is essential to converting between the mass of a substance and the amount in moles - the unit chemists use to count particles like atoms and molecules. This concept can be seen in Step 2 of the example problem, where the mass of iron is converted into moles.
To find the moles of iron, you take the mass (15.5 mg) and convert it to grams (0.0155 g), then divide by the molar mass of iron (55.85 g/mol): \(\frac{0.0155\,\mathrm{g}}{55.85\,\mathrm{g/mol}}\). The same process is used to find how much iron(III) chloride forms, using its molar mass (162.2 g/mol).

• This method is pivotal in stoichiometry to identify the amount of product formed or reactant required.
• It is applicable in various chemical processes where exact measurements are necessary for reactions.

Understanding molar mass calculation is a key skill in chemistry, helping translate between the macroscopic world we see and the atomic-sized world of molecules.