Problem 58 - Chemistry and Chemical Reactivity

Question

A semiconducting material is composed of \(52 \mathrm{g}\) of \(\mathrm{Ga}\), \(9.5 \mathrm{g}\) of \(\mathrm{Al}\), and \(112 \mathrm{g}\) of As. Which element has the largest number of atoms in the final mixture?

Step-by-Step Solution

Answer

Arsenic (As) has the largest number of atoms.

Step 1: Calculate Moles of Each Element

First, find the molar mass of each element: Gallium (Ga) is approximately 69.72 g/mol, Aluminum (Al) is approximately 26.98 g/mol, and Arsenic (As) is approximately 74.92 g/mol. For Ga: Calculate the moles as \( \frac{52}{69.72} \approx 0.746 \) moles. For Al: Calculate the moles as \( \frac{9.5}{26.98} \approx 0.352 \) moles. For As: Calculate the moles as \( \frac{112}{74.92} \approx 1.495 \) moles.

Step 2: Compare Moles to Determine Number of Atoms

Since each mole of a substance contains Avogadro's number of atoms (approximately \(6.022 \times 10^{23}\)), the element with the highest number of moles will have the most atoms. From Step 1: Ga has 0.746 moles, Al has 0.352 moles, and As has 1.495 moles. Therefore, As has the largest number of atoms because 1.495 moles is greater than 0.746 moles and 0.352 moles.

Key Concepts

Molar Mass

The concept of molar mass is crucial in understanding chemistry and performing mole calculations. Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is essentially the molecular weight of a chemical compound or element expressed in terms of grams. To determine the molar mass of an element:

• Look at the periodic table for the atomic mass of the element, usually found below the element symbol.
• This atomic mass, expressed in atomic mass units (amu), will be the molar mass when expressed in grams per mole (g/mol).

For instance, in the original exercise: - Gallium (Ga) has an atomic mass of approximately 69.72, making its molar mass 69.72 g/mol. - Aluminum (Al) has a molar mass of approximately 26.98 g/mol. - Arsenic (As) has a molar mass of approximately 74.92 g/mol. Understanding molar mass allows us to convert between the mass of a substance and the number of moles, which is pivotal in stoichiometric calculations.

Atomic Structure

The atomic structure of an element profoundly impacts its chemical properties, reactivity, and bonding characteristics. It comprises protons, neutrons, and electrons. The protons and neutrons form the atomic nucleus, while the electrons orbit around the nucleus in different energy levels or shells. Key points to consider:

• Atomic Number: It represents the number of protons in an atom. In a neutral atom, it also equals the number of electrons.
• Mass Number: This is the total number of protons and neutrons in the atom's nucleus.
• Isotopes: Atoms of the same element with different numbers of neutrons, leading to different mass numbers.

Understanding the atomic structure helps in predicting how an element will react chemically. For example, the electrons in the outermost energy level (valence electrons) chiefly determine the bonding characteristics and reactivity of the element. These fundamentals of atomic structure play an essential role when we perform chemical calculations, ensuring that our predictions and solutions are accurate.

Mole Calculation

Mole calculations are a fundamental aspect of chemistry that allow us to convert between mass, moles, and number of atoms or molecules. The mole is a bridge concept that ties together the macroscopic quantities we measure with the microscopic countable entities, like atoms and molecules, that undergo chemical reactions.The key to mole calculations is Avogadro's number, which is approximately \(6.022 \times 10^{23}\) atoms/molecules per mole. This allows us to compute the number of representative particles in a given sample:

• To Calculate Moles: Use the formula \( \text{moles} = \frac{\text{mass of the sample} (g)}{\text{molar mass} (g/mol)} \).
• To Calculate Particles: Multiply moles by Avogadro's number.

Applying this to the example given, we calculated the moles of each element:- Ga: \(\frac{52}{69.72} \approx 0.746\) moles.- Al: \(\frac{9.5}{26.98} \approx 0.352\) moles.- As: \(\frac{112}{74.92} \approx 1.495\) moles.Knowing the moles, we determined that Arsenic (As), which has the highest moles, also has the largest number of atoms in the mixture due to the fact that each mole contains the same number of atoms.