Problem 122 - General Chemistry: Principles and Modern Applications

Question

\(\mathrm{XF}_{3}\) consists of \(65 \%\) F by mass. The atomic mass of the element X must be (a) 8 u; (b) 11 u; (c) 31 u; (d) 35 u.

Step-by-Step Solution

Answer

The atomic mass of element X in the \(\mathrm{XF}_{3}\) compound is approximately 31u. Therefore, the correct choice is (c).

Step 1: Identify Given Information

The given information is that \(\mathrm{XF}_{3}\) consists of 65% Fluorine by mass. The atomic mass of Fluorine is 19u.

Step 2: Calculate the Mass of Fluorine in the Compound

Based on the given composition, since there are three atoms of Fluorine in the compound, the total mass of Fluorine is \(3 \times 19u = 57u\).

Step 3: Calculate the Remaining Mass of X

If Fluorine makes up 65% of the compound's mass, then the remaining 35% is element X. Therefore, we can use the equation (mass of compound) = (mass of Fluorine + mass of X) to calculate the mass of X. The total mass is \( \frac{57u}{0.65} \approx 87.69u\), which makes the mass of X approximately \(87.69u - 57u = 30.69u\).

Step 4: Identify the Accurate Atomic Mass

Looking at the options, the atomic mass of X that is closest to the calculated mass is 31u, which means the correct choice is (c).

Key Concepts

Chemical Composition

Understanding the chemical composition of a compound involves knowing what elements are present and in what proportions. In \(XF_3\), the formula tells us that there is one atom of element X and three atoms of fluorine. This means the chemical structure consists of these four atoms bonded together.

By examining the formula, scientists can predict the mass contributions of each element to the total. This provides insight into the compound's properties, like its reactivity and stability.

• Element X: 1 atom
• Fluorine: 3 atoms

Understanding the atomic makeup lays the foundation for more complex calculations, such as finding mass percentages.

Mass Percentage

Mass percentage is a way of expressing how much of a particular element is present in a compound in terms of its mass fraction. In \(XF_3\), the problem states that fluorine makes up 65% of the compound's mass. This means for every 100 units of mass of \(XF_3\), 65 units come from fluorine.

Calculating mass percentages involves comparing the mass of the desired element to the total mass of the compound and expressing it as a percentage. The formula for finding mass percentage is:

\[ \text{Mass Percentage} = \left( \frac{\text{mass of element}}{\text{total mass of compound}} \right) \times 100\]

• Calculate the mass of the element in the compound.
• Find the total mass of the compound.
• Apply the formula to find the percentage.

Using mass percentage is crucial in chemistry as it helps to analyze the composition without needing to know the exact quantities present.

Fluorine

Fluorine is a highly reactive and electronegative element, represented by the symbol F, and has an atomic mass of 19 u. In compounds like \(XF_3\), fluorine often exerts a significant influence due to these chemical properties. Here, it's responsible for 65% of the compound's mass.

Understanding fluorine's role in such compounds helps in predicting its behavior under different conditions, such as reactions with other elements. Fluorine's reactivity stems largely from its electronegativity, making it a key contributor in many chemical processes.

• Symbol: F
• Atomic Mass: 19 u
• Role in \(XF_3\): Comprises a majority of compound's mass

Knowing these basic characteristics of fluorine allows students to better understand its interactions and importance in different compounds.