Problem 49 - Chemistry: The Central Science

Question

A compound whose empirical formula is \(\mathrm{XF}_{3}\) consists of \(65 \%\) \(F\) by mass. What is the atomic mass of \(X\) ?

Step-by-Step Solution

Answer

The atomic mass of element \(X\) in the compound \(\mathrm{XF_{3}}\) is approximately \(30.69 \, \text{amu}\).

Step 1: Calculate the mass of 3 F atoms

First, let's find the mass of 3 F atoms. The atomic mass of F (Fluorine) is \(19 \, \text{amu}\). We have 3 F atoms in our empirical formula, and their combined mass will be: \(3 \times 19 \, \text{amu} = 57 \, \text{amu}\).

Step 2: Calculate the mass percentage of X in the compound

We know that the mass percentage of F in the compound is \(65 \%\). So, the mass percentage of X in the compound will be: \(100 \% - 65 \% = 35 \%\).

Step 3: Calculate the total mass of the compound

Now let's denote the total mass of the compound as M. As we are given the mass percentages, we can write: \(\frac{57 \, \text{amu}}{\text{M}} = 0.65\). Solving for M, \(\text{M} = \frac{57 \, \text{amu}}{0.65} \approx 87.69 \, \text{amu}\).

Step 4: Calculate the atomic mass of X

Finally, we can find the atomic mass of X. We know that 35% of the compound's mass is attributed to X: \(\frac{\text{mass of X}}{87.69 \, \text{amu}} = 0.35\). Solving for the mass of X, \(\text{mass of X} = 0.35 \times 87.69 \, \text{amu} \approx 30.69 \, \text{amu}\). Therefore, the atomic mass of element \(X\) is approximately \(30.69 \, \text{amu}\).

Key Concepts

Atomic Mass

Atomic mass is a measure of the mass of an individual atom of a chemical element. It’s usually measured in atomic mass units (amu). Each element's atomic mass is roughly equal to the number of protons and neutrons it contains. For example, the atomic mass of fluorine (\(F\)) is 19 amu. This number is critical when calculating the overall mass of a compound. In our exercise, finding the atomic mass of element \(X\) requires understanding how it relates to the mass of fluorine within the compound.

Knowing the atomic mass allows us to make comparisons between elements and to calculate the molecular or empirical formulas for compounds. This is essential for understanding how different elements combine to form various chemical compounds.

Mass Percentage

Mass percentage, also known as percent composition, is used to describe the concentration of an element in a compound. It's calculated by dividing the mass of the element by the total mass of the compound and then multiplying by 100 to get a percentage. For example, if 65% of our compound's mass comes from fluorine, then 35% comes from the unknown element \(X\).

Here's how you calculate the mass percentage:

• Determine the mass of each component in the compound.
• Divide the mass of the individual element by the compound's total mass.
• Multiply by 100 to get a percentage.

Mass percentage helps chemists determine the formula of a compound and identify how much of each element is present. This is crucial for the proper identification and analysis of unknown substances.

Compound Calculation

Compound calculations involve determining the total mass and the composition of a compound based on given data. In the exercise, we approached this by first finding the total mass of the compound using the mass percentages. We isolated the mass of each component, known elements like fluorine, and used the relative mass percentages to find the unknown.

Steps to follow in compound calculation:

• Calculate the combined mass of known elements like the three fluorine atoms.
• Use the given mass percentages to set up equations relating the total mass to the known components.
• Solve these equations to find the total mass and then the atomic mass of the unknown element \(X\).

These calculations are vital to understanding molecular structures and ensuring the accurate synthesis and analysis of compounds in both lab and industry settings.