Problem 31 - Chemistry and Chemical Reactivity

Question

You are given 1.0 -g samples of He, Fe, \(\mathrm{I}\) i, \(\mathrm{Si}\), and \(\mathrm{C}\). Which sample contains the largest number of atoms? Which contains the smallest?

Step-by-Step Solution

Answer

He has the most atoms; I has the fewest.

Step 1: Find Molar Masses

Determine the molar masses of each element using the periodic table: - He: 4.00 g/mol - Fe: 55.85 g/mol - I: 126.90 g/mol - Si: 28.09 g/mol - C: 12.01 g/mol.

Step 2: Calculate Moles for Each Sample

Use the formula \( \, \text{moles} = \frac{\text{mass}}{\text{molar mass}} \, \) to calculate moles for each sample.- He: \( \frac{1.0 \, \text{g}}{4.00 \, \text{g/mol}} = 0.25 \, \text{mol} \)- Fe: \( \frac{1.0 \, \text{g}}{55.85 \, \text{g/mol}} \approx 0.0179 \, \text{mol} \)- I: \( \frac{1.0 \, \text{g}}{126.90 \, \text{g/mol}} \approx 0.00788 \, \text{mol} \)- Si: \( \frac{1.0 \, \text{g}}{28.09 \, \text{g/mol}} \approx 0.0356 \, \text{mol} \)- C: \( \frac{1.0 \, \text{g}}{12.01 \, \text{g/mol}} \approx 0.0833 \, \text{mol} \).

Step 3: Identify the Largest and Smallest Number of Atoms

Since the number of atoms is directly proportional to the number of moles, the sample with the most moles has the largest number of atoms, and the one with the least moles has the smallest number of atoms. - He: 0.25 mol - Fe: 0.0179 mol - I: 0.00788 mol - Si: 0.0356 mol - C: 0.0833 mol He contains the largest number of atoms, and I contains the smallest.

Key Concepts

Moles Conversion

When dealing with chemical elements, converting mass to moles is a foundational skill in chemistry. Moles represent a quantity of substance, specifically counting the number of particles, like atoms or molecules, in a sample. The conversion from mass to moles is accomplished using the formula:\[\text{moles} = \frac{\text{mass}}{\text{molar mass}}\]The mass is usually given in grams, and the molar mass is obtained from the periodic table, measured in grams per mole (g/mol).
For instance, with a 1.0 g sample of Helium (He) and a molar mass of 4.00 g/mol, the conversion would be:

• \( \frac{1.0 \, \text{g}}{4.00 \, \text{g/mol}} = 0.25 \, \text{mol} \)

This process allows us to work with quantities that, although hard to grasp on a molecular scale, make much more sense in practical laboratory terms. By converting mass to moles, we bridge the gap between tiny atoms and something countable.

Number of Atoms

Once you have calculated the moles of a substance, it becomes straightforward to find the number of atoms using Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles/mol. This constant tells us how many atoms are in one mole. Thus, the total number of atoms in a sample is given by:\[\text{Number of Atoms} = \text{moles} \times 6.022 \times 10^{23}\]For example, if we have 0.25 moles of He, it contains:

• \(0.25 \times 6.022 \times 10^{23}\) atoms, which approximately equals \(1.506 \times 10^{23}\) atoms.

This illustrates how conversions facilitate understanding of how many atoms are present in given amounts of substances, making abstract molecular scale concepts accessible.

Periodic Table Elements

The periodic table is an essential tool in calculating molar mass, which is a stepping stone to converting mass to moles and eventually determining the number of atoms. Each element on the periodic table lists its atomic number and atomic mass. The atomic mass tells us the weight of one mole of atoms for that element, in g/mol.
Here are some examples from the problem:

• Helium (He): 4.00 g/mol
• Iron (Fe): 55.85 g/mol
• Iodine (I): 126.90 g/mol
• Silicon (Si): 28.09 g/mol
• Carbon (C): 12.01 g/mol

These values are crucial when converting grams to moles. Understanding and utilizing the periodic table for these conversions allows us to accurately determine quantitative information about chemical reactions and structures in both classroom and laboratory settings.