Question

Calculate the mass in grams of iodine \(\left(\mathrm{I}_{2}\right)\) that will react completely with \(20.4 \mathrm{~g}\) of aluminum (Al) to form aluminum iodide \(\left(\mathrm{AlI}_{3}\right)\).

Short answer

The mass of iodine needed is approximately 288.01 grams.

Step-by-step solution

Write the Balanced Chemical Equation

To solve the problem, we first need the balanced chemical equation for the reaction of aluminum (Al) with iodine (\(\mathrm{I}_{2}\). The balanced equation is: \[ 2\mathrm{Al} + 3\mathrm{I}_{2} \rightarrow 2\mathrm{AlI}_{3} \] This equation indicates that 2 moles of aluminum react with 3 moles of iodine to form 2 moles of aluminum iodide.

Calculate Moles of Aluminum

The moles of a substance can be calculated using its mass and molar mass. The molar mass of aluminum (Al) is \(26.98\,\mathrm{g/mol}\). Thus, the moles of aluminum are: \[\text{Moles of } \mathrm{Al} = \frac{20.4\,\mathrm{g}}{26.98\,\mathrm{g/mol}} \approx 0.756\,\mathrm{mol} \]

Use Stoichiometry to Find Moles of Iodine

From the balanced equation in Step 1, \(2\) moles of \(\mathrm{Al}\) react with \(3\) moles of \(\mathrm{I}_{2}\). Thus, \(0.756\) moles of \(\mathrm{Al}\) will react with: \[ \text{Moles of } \mathrm{I}_{2} = \frac{3}{2} \times 0.756\,\mathrm{mol} \approx 1.134\,\mathrm{mol} \]

Calculate Mass of Iodine

The molar mass of iodine \(\mathrm{I}_{2}\) is \(253.81\,\mathrm{g/mol}\). Using the moles of iodine calculated in Step 3, we find the mass of iodine needed: \[ \text{Mass of } \mathrm{I}_{2} = 1.134\,\mathrm{mol} \times 253.81\,\mathrm{g/mol} \approx 288.01\,\mathrm{g} \]

Key concepts

Balanced Chemical Equation

A balanced chemical equation is essential for understanding the proportions in which substances react with each other. For any reaction, it shows the number of moles of reactants and products involved. In our exercise, we examine the reaction between aluminum (Al) and molecular iodine \(\mathrm{I}_2\). The balanced chemical equation for this reaction is:
\[ 2\mathrm{Al} + 3\mathrm{I}_2 \rightarrow 2\mathrm{AlI}_3 \]
This equation tells us that 2 moles of aluminum react with 3 moles of iodine to produce 2 moles of aluminum iodide (\(\mathrm{AlI}_3\)). Understanding this relation is the first step in solving stoichiometry problems. It provides the framework needed for calculating how much of each reactant is required or how much product is formed. By interpreting the coefficients, we can determine the exact quantities needed for complete conversions without any excess reactants left over.

Moles Calculation

Moles calculation is a fundamental concept in stoichiometry. It involves calculating the number of moles of a substance when given its mass and molar mass. This step is crucial because chemical reactions occur in definite mole ratios. To determine the moles of aluminum in our example, we use its mass, 20.4 grams, and its molar mass, approximately 26.98 \(\mathrm{g/mol}\).
Here's how we calculate it:

• First, use the formula: \(\text{Moles of } \mathrm{Al} = \frac{\text{mass of Al}}{\text{molar mass of Al}}\)
• Substituting the given values, we find: \(\text{Moles of Al} = \frac{20.4 \, \mathrm{g}}{26.98 \, \mathrm{g/mol}} \approx 0.756 \, \mathrm{mol}\)

This calculation gives us the number of moles of aluminum that will participate in the reaction. The mole ratio provided by the chemical equation will then help us find the corresponding moles of iodine required.

Aluminum Reaction

The reaction of aluminum with iodine is an example of a synthesis reaction, where two or more substances combine to form a single product. In this exercise, aluminum (Al) reacts with iodine \(\mathrm{I}_2\) to form aluminum iodide \(\mathrm{AlI}_3\).Let's break it down:

• The balanced reaction equation, \(2\mathrm{Al} + 3\mathrm{I}_2 \rightarrow 2\mathrm{AlI}_3\), shows that aluminum and iodine are consumed in a \(2:3\) mole ratio.
• This tells us that for every 2 moles of aluminum, 3 moles of iodine are required.
• We calculated, in the exercise, that 0.756 moles of aluminum will need to react, which requires applying this ratio to find the moles of iodine.

Hence, this ratio is key to determining how much iodine should be present to completely react with the given amount of aluminum.

Iodine Mass Calculation

Calculating the mass of iodine required in a chemical reaction involves using the mole concept and the reaction's stoichiometry. We've already determined that 1.134 moles of iodine are needed for the reaction with our calculated amount of aluminum.Here’s how to calculate the iodine's mass:

• The molar mass of iodine (\(\mathrm{I}_2\)) is known to be 253.81 \(\mathrm{g/mol}\).
• By multiplying the moles of iodine by its molar mass, we can find the mass: \(\text{Mass of } \mathrm{I}_2 = 1.134 \, \mathrm{mol} \times 253.81 \, \mathrm{g/mol} = 288.01 \, \mathrm{g}\).

Thus, approximately 288 grams of iodine are required to react completely with 20.4 grams of aluminum. This calculation is crucial in practical scenarios, ensuring that all reactants are used efficiently without wastage.