Question

Using the average atomic masses given inside the front cover of this book, calculate the number of atoms present in each of the following samples. a. \(1.50 \mathrm{~g}\) of silver, \(\mathrm{Ag}\) b. 0.0015 mole of copper, \(\mathrm{Cu}\) c. 0.0015 g of copper, \(\mathrm{Cu}\) d. \(2.00 \mathrm{~kg}\) of magnesium, \(\mathrm{Mg}\) e. 2.34 oz of calcium, Ca f. 2.34 g of calcium, Ca g. 2.34 moles of calcium, Ca

Short answer

The number of atoms in each sample are as follows: a. \(8.37\times 10^{21}\) Ag atoms b. \(9.033\times 10^{20}\) Cu atoms c. \(1.42\times 10^{19}\) Cu atoms d. \(4.95\times 10^{25}\) Mg atoms e. \(9.97\times 10^{23}\) Ca atoms f. \(3.51\times 10^{22}\) Ca atoms g. \(1.41\times 10^{24}\) Ca atoms

Step-by-step solution

Identify the average atomic mass and given information for each element

Use the average atomic masses given inside the front cover of the book to identify the necessary information. a. Ag: Average atomic mass = 107.87 g/mol b. Cu: Average atomic mass = 63.55 g/mol c. Cu: Average atomic mass = 63.55 g/mol d. Mg: Average atomic mass = 24.31 g/mol e. Ca: Average atomic mass = 40.08 g/mol f. Ca: Average atomic mass = 40.08 g/mol g. Ca: Average atomic mass = 40.08 g/mol

Find moles for samples given in grams

For samples a, c, d, e, and f, we are given the mass in grams, which we need to convert to moles before we calculate the number of atoms. Use the equation: Moles = (Given mass in grams) / (Average atomic mass in g/mol) a. Moles of Ag: \(\frac{1.5}{107.87} = 0.0139\) moles c. Moles of Cu: \(\frac{0.0015}{63.55} = 2.362\times 10^{-5}\) moles d. Moles of Mg: \(\frac{2000}{24.31} = 82.259\) moles e. Convert oz to grams first: 2.34 oz * 28.3495 g/oz = 66.337 g Moles of Ca: \(\frac{66.337}{40.08} = 1.655\) moles f. Moles of Ca: \(\frac{2.34}{40.08} = 0.0583\) moles

Calculate the number of atoms using Avogadro's Number

Now, we can convert moles to atoms using Avogadro's Number, which is \(6.022\times 10^{23}\) atoms/mol. Number of atoms = (Moles) * (Avogadro's Number) a. Number of Ag atoms: \(0.0139\times 6.022\times 10^{23}\) = \(8.37\times 10^{21}\) Ag atoms b. Number of Cu atoms: \(0.0015\times 6.022\times 10^{23}\) = \(9.033\times 10^{20}\) Cu atoms c. Number of Cu atoms: \(2.362\times 10^{-5}\times 6.022\times 10^{23}\) = \(1.42\times 10^{19}\) Cu atoms d. Number of Mg atoms: \(82.259\times 6.022\times 10^{23}\) = \(4.95\times 10^{25}\) Mg atoms e. Number of Ca atoms: \(1.655\times 6.022\times 10^{23}\) = \(9.97\times 10^{23}\) Ca atoms f. Number of Ca atoms: \(0.0583\times 6.022\times 10^{23}\) = \(3.51\times 10^{22}\) Ca atoms g. Number of Ca atoms: \(2.34\times 6.022\times 10^{23}\) = \(1.41\times 10^{24}\) Ca atoms

Key concepts

Atomic Mass

Atomic mass is a crucial concept in chemistry that refers to the mass of an atom expressed in atomic mass units (amu). This value is often found on the periodic table and helps to understand how much one mole of an element weighs in grams. An atomic mass unit is equivalent to one-twelfth the mass of one carbon-12 atom.

For example:

• Silver (Ag) has an atomic mass of 107.87 g/mol.
• Copper (Cu) has an atomic mass of 63.55 g/mol.
• Magnesium (Mg) has an atomic mass of 24.31 g/mol.
• Calcium (Ca) has an atomic mass of 40.08 g/mol.

The atomic mass helps in converting between the mass of a substance and the amount in moles through simple arithmetic division. When we know the mass of an element and its atomic mass, we can easily find out how many moles of atoms there are by dividing the mass of the sample by the atomic mass. Thus, atomic mass is fundamental for understanding chemical quantities and stoichiometry.

Mole Conversions

Mole conversions are essential in translating the mass of a substance to another useful measure, moles, which relates directly to the number of atoms or molecules. To perform a mole conversion, follow this formula: \[ \text{Moles} = \frac{\text{Given mass in grams}}{\text{Atomic mass in g/mol}} \] Let's break down these calculations:

• Convert a mass in grams to moles by using the element's atomic mass.
• Make sure to match the units — grams in the numerator and g/mol in the denominator cancels the unit of grams, leaving you with moles.

In the case of different metals, consider converting common masses such as 2.34 ounces to grams if required. Once you have determined the number of moles, you can use mole conversions to find the number of atoms by multiplying by Avogadro’s number, \( 6.022 \times 10^{23} \) atoms/mol. These conversions are key in stoichiometry for both calculations and experiments.

Elementary Particles

Elementary particles are the smallest known building blocks of matter and include protons, neutrons, and electrons in atoms. Understanding how many atoms are in a sample involves dealing with these particles at a very large scale, as represented by Avogadro’s number, \( 6.022 \times 10^{23} \). _{Avogadro's number is a crucial constant that gives the number of particles in one mole of a substance.} This allows chemists to transition from measuring masses in the lab to counting atoms and molecules in a theoretical sense.In the calculation, when you have the number of moles, multiplying by Avogadro's number gives you the total number of elementary particles, specifically atoms in this context, present in the sample. For example, if you calculate that you have 0.0139 moles of silver, then the particle count is calculated as follows:

• \(0.0139 \times 6.022 \times 10^{23} = 8.37 \times 10^{21}\) atoms of silver

These elementary particles are what make up atoms, and understanding their numbers and interactions helps in comprehending the larger structure of substances.