Question

A piece of aluminum foil \(1.00 \mathrm{~cm}\) square and \(0.550 \mathrm{~mm}\) thick is allowed to react with bromine to form aluminum bromide as shown in the accompanying photo. (a) How many moles of aluminum were used? (The density of aluminum is \(2699 \mathrm{~g} / \mathrm{cm}^{3}\) ) (b) How many grams of aluminum bromide form, assuming the aluminum reacts completely?

Short answer

(a) 5.48 moles of aluminum were used. (b) 1461 grams of aluminum bromide will form.

Step-by-step solution

Calculate the mass of aluminum

To calculate the mass of aluminum, use the formula: mass = volume × density First, find the volume of the aluminum piece by multiplying its dimensions: volume = length × width × height volume = \(1.00 ~ cm × 1.00 ~ cm × 0.0550 ~ cm = 0.0550 ~ cm^3\) Next, use the given density to find the mass: mass = \(0.0550 ~ cm^3 × 2699 ~ g/cm^3 = 148 ~ g\)

Convert mass of aluminum to moles

To convert the mass of aluminum to moles, use the molar mass of aluminum. The molar mass of aluminum is approximately 26.98 g/mol. moles of Al = mass of Al / molar mass of Al moles of Al = \(148 ~ g / 26.98 ~ g/mol = 5.48 ~ mol\)

Calculate the mass of aluminum bromide formed

The balanced chemical equation for the reaction between aluminum and bromine is: \(2Al + 3Br_2 → 2AlBr_3\) From the balanced equation, we can see that 2 moles of aluminum react completely with 3 moles of bromine to form 2 moles of aluminum bromide. Therefore, for every mole of aluminum, we have 1 mole of aluminum bromide. moles of AlBr3 = moles of Al moles of AlBr3 = 5.48 mol Now, we need to convert the moles of aluminum bromide to grams using its molar mass. The molar mass of aluminum bromide (AlBr3) is approximately 266.69 g/mol. mass of AlBr3 = moles of AlBr3 × molar mass of AlBr3 mass of AlBr3 = \(5.48 ~ mol × 266.69 ~ g/mol = 1461 ~ g\) So, when the aluminum reacts completely, 1461 grams of aluminum bromide will form. The final answers are: (a) 5.48 moles of aluminum were used. (b) 1461 grams of aluminum bromide will form.

Key concepts

Chemical Reactions

Chemical reactions involve the transformation of reactants into products through the breaking and forming of chemical bonds. In this reaction, aluminum (Al) reacts with bromine (\( \text{{Br}}_2 \)) to form aluminum bromide (\( \text{{AlBr}}_3 \)). This is a classic example of a synthesis reaction, where simpler substances combine to create a more complex compound.
To understand the stoichiometry of the reaction, it is critical to look at the balanced chemical equation:
\[2 \text{{Al}} + 3 \text{{Br}}_2 \rightarrow 2 \text{{AlBr}}_3\]
This equation tells us that two moles of aluminum react with three moles of bromine to produce two moles of aluminum bromide.
The coefficients in the equation indicate the molar ratio between the reactants and the products. It means for every two moles of aluminum, you get two moles of aluminum bromide, maintaining the 1:1 molar relationship between them.

Molar Mass

Molar mass is a fundamental concept in chemistry that helps in converting between a substance’s mass and the amount of substance (in moles). Every element has a unique molar mass, which is essentially the mass of one mole of that element's atoms.
For aluminum (Al), the molar mass is approximately 26.98 grams per mole. This means that 26.98 grams of aluminum is equivalent to one mole of aluminum atoms. The calculated amount of aluminum used was 148 grams, so dividing this by the molar mass helps find the number of moles of aluminum:
\[\text{{Moles of Al}} = \frac{{148 \, \text{grams}}}{{26.98 \, \text{g/mol}}} = 5.48 \, \text{moles}\]
Similarly, for aluminum bromide (\(\text{AlBr}_3\)), the molar mass is calculated by adding the atomic masses of three bromine atoms and one aluminum atom. It's about 266.69 grams per mole.
Understanding molar mass allows us to determine the mass of a desired product when moles are known or vice versa, which is crucial in many areas of chemistry research and industry.

Density Calculations

Density is a key property of materials and describes how much mass is packed into a given volume. It's defined as mass per unit volume. For solid materials like the aluminum foil in the exercise, density is used to find out how much material is present in a piece with known volume.
The formula for calculating density (\( \rho \)) is:
\[ \rho = \frac{{\text{mass}}}{{\text{volume}}} \]
For the piece of aluminum in this problem, the density is given as 2699 grams per cubic centimeter. To find the mass of aluminum, you multiply this density by the volume:
First, determine the volume:
Volume = 1.00 cm × 1.00 cm × 0.0550 cm = 0.0550 cm³
Then, calculate the mass using the density:
Mass = 0.0550 cm³ × 2699 g/cm³ = 148 grams
Density calculations are crucial for determining how much of a material is present without directly measuring the weight, a useful attribute in many scientific and engineering applications.