Question

Iron metal reacts with chlorine gas. How many grams of \(\mathrm{FeCl}_{3}\) are obtained when \(515 \mathrm{g} \mathrm{Cl}_{2}\) reacts with excess Fe? $$ 2 \mathrm{Fe}(\mathrm{s})+3 \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{FeCl}_{3}(\mathrm{s}) $$

Short answer

783.6 grams of FeCl3 can be produced.

Step-by-step solution

Determine the molar mass of Cl2 and FeCl3

From the periodic table, the molar mass of Cl is approximately 35.5 g/mol. Therefore the molar mass of Cl2 is \(35.5 g/mol * 2 = 71 g/mol\). The molar mass of FeCl3 is \(55.85 g/mol + 35.5 g/mol * 3 = 162.2 g/mol\). This is the number of grams per mole for each substance.

Convert mass of Cl2 to moles

The mass of Cl2 given is 515g. To convert this mass to moles, we use the molar mass from step 1. Therefore, the number of moles of Cl2 is \(515g ÷ 71g/mol = 7.25 mol\). This is how many moles of Cl2 we have.

Use stoichiometry to find moles of FeCl3

By looking at the balanced chemical equation, we can see that for every 3 moles of Cl2, 2 moles of FeCl3 are produced. Therefore, we can create a stoichiometric ratio and multiply it by the moles of Cl2 to find the moles of FeCl3. The number of moles of FeCl3 is \(7.25 mol * 2/3 = 4.83 mol\). This is how many moles of FeCl3 we can produce.

Convert moles of FeCl3 to grams

To find the mass of FeCl3 produced, we use the molar mass of FeCl3 from step 1 and multiply it by the moles of FeCl3. The mass of FeCl3 is \(4.83 mol * 162.2 g/mol = 783.6 g\). This is how many grams of FeCl3 we can produce.

Key concepts

Molar Mass Calculations

Molar mass is a key concept in stoichiometry, allowing the conversion of moles to grams and vice-versa. The molar mass of an element is the mass of one mole of its atoms and is usually expressed in grams per mole (g/mol). An element's molar mass can be found on the periodic table, where each element's typical atomic weight is listed.

For compounds, the molar mass is the sum of the molar masses of all the atoms in the molecule. For example, the molar mass of chlorine gas \(\mathrm{Cl}_2\) is calculated by multiplying the molar mass of one chlorine atom, which is about 35.5 g/mol, by two, resulting in 71 g/mol. Similarly, the molar mass of iron(III) chloride \(\mathrm{FeCl}_3\) is calculated by adding the molar mass of one iron atom (55.85 g/mol) to the molar masses of three chlorine atoms (3 x 35.5 g/mol), which totals 162.2 g/mol.

Understanding molar masses is crucial for converting between the mass of a substance and the moles of that substance, a central focus in stoichiometry.

Chemical Reactions

Chemical reactions can be thought of as processes where substances, known as reactants, are transformed into new substances called products. This transformation is depicted by chemical equations, which include the reactants on the left side and the products on the right. A balanced chemical equation shows the relationship between the number of moles of reactants and products, which is essential in stoichiometry.

In the reaction between iron metal and chlorine gas, represented as: \[ 2 \mathrm{Fe}(\mathrm{s}) + 3 \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{FeCl}_{3}(\mathrm{s}) \] the balanced equation indicates that three moles of chlorine gas react with two moles of iron to produce two moles of iron(III) chloride.

This stoichiometric ratio helps in determining how much product can be formed from a given amount of reactant. By understanding the relationship between reactants and products, chemists can predict the amounts of substances consumed and produced in a chemical reaction.

Conversion of Moles to Grams

Converting moles to grams is essential in stoichiometry to quantify chemical reactions. It involves using the concept of molar mass to translate the amount of substance in moles into its equivalent mass in grams.

The conversion process is straightforward: multiply the number of moles of a substance by its molar mass. For example, if there are 4.83 moles of \(\mathrm{FeCl}_3\), and knowing its molar mass is 162.2 g/mol, the calculation becomes \(4.83 \text{ mol} \times 162.2 \text{ g/mol} = 783.6 \text{ g}\). Thus, 4.83 moles of iron(III) chloride is equivalent to 783.6 grams.

This conversion shows how stoichiometric problems in chemistry frequently require shifting between moles and grams, using the molar mass as the conversion factor. It's these conversions that help calculate the mass of reactants needed or products formed during a chemical reaction.