Problem 65 - Chemistry and Chemical Reactivity

Question

You are given 1.0 -g samples of He, Fe, Li, Si, and C. Which sample contains the largest number of atoms? Which contains the smallest?

Step-by-Step Solution

Answer

Helium contains the largest number of atoms; Iron contains the smallest.

Step 1: Use Molar Mass to Convert Grams to Moles

Determine the molar mass of each element (He, Fe, Li, Si, C) using the periodic table: He = 4.00 g/mol, Fe = 55.85 g/mol, Li = 6.94 g/mol, Si = 28.09 g/mol, C = 12.01 g/mol. Use the formula \( \text{moles} = \frac{\text{grams}}{\text{molar mass}} \) to convert grams to moles for each element.

Step 2: Calculate Moles of Each Element

For 1.0 g of each element, calculate the moles:- He: \( \frac{1.0 \text{ g}}{4.00 \text{ g/mol}} = 0.25 \text{ moles}\)- Fe: \( \frac{1.0 \text{ g}}{55.85 \text{ g/mol}} = 0.0179 \text{ moles}\)- Li: \( \frac{1.0 \text{ g}}{6.94 \text{ g/mol}} = 0.144 \text{ moles}\)- Si: \( \frac{1.0 \text{ g}}{28.09 \text{ g/mol}} = 0.0356 \text{ moles}\)- C: \( \frac{1.0 \text{ g}}{12.01 \text{ g/mol}} = 0.0833 \text{ moles}\)

Step 3: Use Avogadro's Number for Atom Count

Each mole contains Avogadro's number of atoms, \( 6.022 \times 10^{23} \) atoms/mole. Multiply the moles by Avogadro's number to find the number of atoms for each:- He: \( 0.25 \times 6.022 \times 10^{23} = 1.51 \times 10^{23} \) atoms- Fe: \( 0.0179 \times 6.022 \times 10^{23} = 1.08 \times 10^{22} \) atoms- Li: \( 0.144 \times 6.022 \times 10^{23} = 8.67 \times 10^{22} \) atoms- Si: \( 0.0356 \times 6.022 \times 10^{23} = 2.14 \times 10^{22} \) atoms- C: \( 0.0833 \times 6.022 \times 10^{23} = 5.02 \times 10^{22} \) atoms

Step 4: Determine the Largest and Smallest Atom Counts

Compare the calculated atom counts:- Largest: Helium (He) with \( 1.51 \times 10^{23} \) atoms.- Smallest: Iron (Fe) with \( 1.08 \times 10^{22} \) atoms.

Key Concepts

Molar Mass

Molar mass is an essential concept in chemistry that allows you to relate the mass of a substance to the amount of substance it contains, measured in moles. Each element has a unique molar mass, which can be found on the periodic table and is expressed in units of grams per mole (g/mol). The molar mass value represents the mass in grams of one mole of that particular element or compound.

To calculate how many moles you have from a given mass of an element, you use the formula:

• \( \text{moles} = \frac{\text{grams}}{\text{molar mass}} \)

For example, to find the moles of carbon (C) from a 1.0 g sample, with its molar mass being 12.01 g/mol, you apply the formula and get approximately 0.0833 moles. This method can be applied to any element once you have its molar mass.

Atoms to Moles Conversion

The conversion between atoms and moles is crucial for understanding the size of a sample in terms of the number of particles it contains. This conversion uses Avogadro's number, which is approximately \( 6.022 \times 10^{23} \) atoms/mol. This number tells you how many atoms or molecules are in one mole of a substance.

If you know the number of moles but want to find out the number of atoms, multiply the number of moles by Avogadro's number:

• \( \text{atoms} = \text{moles} \times 6.022 \times 10^{23} \)

For example, if you have 0.25 moles of helium (He), you can calculate the number of atoms as \( 0.25 \times 6.022 \times 10^{23} = 1.51 \times 10^{23} \). This conversion is key when comparing substances to determine which has more atoms in a given mass.

Periodic Table

The periodic table is an organized chart of all known elements, arranged by increasing atomic number. Each element on the table provides important information, such as atomic number, symbol, name, and atomic mass (related to molar mass). The periodic table is a powerful tool for chemists that helps in understanding the relationships between different elements and their properties.

When you need to find the molar mass of an element for a calculation, look for its atomic mass on the periodic table, as this value usually matches the molar mass for elements in their atomic form. Elements like hydrogen (H), oxygen (O), and carbon (C) are found directly with their standards molar masses.

• Helium (He) has a molar mass of 4.00 g/mol.
• Iron (Fe) has a molar mass of 55.85 g/mol.
• Carbon (C) has a molar mass of 12.01 g/mol.

Understanding how to use the periodic table is essential for calculating the amount of substances in chemical reactions and for converting between mass and moles efficiently.