Problem 3 - Introductory Chemistry Atoms First

Question

A \(101.96-\mathrm{g}\) sample of a compound of aluminum and oxygen is \(47.1 \%\) by mass oxygen. (a) What is the percent by mass aluminum in this compound? (b) Of the \(101.96 \mathrm{~g}\) of this compound, how many grams are aluminum?

Step-by-Step Solution

Answer

(a) The percent by mass of aluminum in the compound is \(52.9\%\). (b) The mass of aluminum in the \(101.96 \mathrm{~g}\) sample of the compound is \(53.94 \mathrm{~g}\).

Step 1: Calculate the mass percentage of aluminum

Since we know the compound is 47.1% oxygen by mass, and there are only two elements in the compound (aluminum and oxygen), we can calculate the mass percentage of aluminum as follows: Percent by mass of aluminum = 100% - Percent by mass of oxygen = 100% - 47.1% = 52.9%.

Step 2: Calculate the mass of aluminum in the compound

Next, we can use the mass percentage of aluminum (52.9%) to find the mass of aluminum in the 101.96-g sample: Mass of aluminum = (Mass percentage of aluminum x Total mass of the compound) / 100% = (52.9% x 101.96 g) / 100% = 53.94 g. Therefore: (a) The percent by mass of aluminum in the compound is 52.9%. (b) The mass of aluminum in the 101.96-g sample of the compound is 53.94 g.

Key Concepts

Aluminum and Oxygen Compound

To better grasp the exercise, let's explore the nature of a compound composed of aluminum and oxygen. Such compounds typically form through chemical reactions between aluminum and oxygen, commonly producing aluminum oxide. Aluminum oxide has a chemical formula of \( \text{Al}_2\text{O}_3 \), indicating that it consists of two aluminum atoms for every three oxygen atoms.
Compounds are substances formed from two or more elements chemically bonded together. In this specific case, only aluminum and oxygen are present in the compound. This makes the calculation of mass percentages straightforward, as the total mass percentage will always add up to 100%.
By understanding the basic nature of an aluminum and oxygen compound, you’re not only preparing to tackle chemistry problems involving such compounds but also building comprehension about how compounds are structured.

Mass Calculation

Mass calculation is a common task in chemistry, particularly when determining the composition of a compound. In this exercise, one essential task is to find the mass percentage of each element in the compound.
Since we are given that the compound is \(47.1\%\) oxygen by mass, the rest of the compound must be aluminum, since these are the only two elements present:

• Percent by mass of aluminum = \(100\% - 47.1\% = 52.9\%\)

This straightforward calculation method demonstrates the concept of conservation of mass within a compound. If you know the percentage of one element, the rest is simply the remaining percentage to reach a total of 100%.
Next, to determine the mass of aluminum in a given sample of the compound, use the percentage value with the total mass:

• Mass of aluminum = \((52.9 \times 101.96 \text{ g}) / 100\% = 53.94 \text{ g}\)

This step involves using a decimal conversion of the percentage to find how much of the compound's mass is composed of aluminum.

Chemistry Problems

Solving chemistry problems involves systematic approaches and methods to find the required solutions. A typical chemistry problem, like the current one involving calculating mass percentages and constituent masses of an aluminum and oxygen compound, illustrates several key steps.
1. **Identify the knowns and unknowns:** - We know the total mass of the compound and its percentage composition. - We need to find the missing values: percent by mass of aluminum and its mass in grams. 2. **Apply fundamental principles:** - Use mass percentages to recognize the proportions of elements present. - Leverage arithmetic to derive one element’s proportion if the other is known, remembering that compositions sum to 100%. 3. **Calculation and verification:** - Perform the calculations as described. - Double-check results for logical consistency and precision.
Encountering various problems strengthens your mastery over chemistry, fortifying your confidence in tackling different challenges. This exercise simplifies complex ideas into an approachable format, making chemistry less intimidating and more engaging.