Problem 93 - Chemistry Matter and Change

Question

Determine the number of moles in each substance. a. \(3.25 \times 10^{20}\) atoms of lead b. \(4.96 \times 10^{24}\) molecules of glucose c. \(1.56 \times 10^{23}\) formula units of sodium hydroxide d. \(1.25 \times 10^{25}\) copper (II) ions

Step-by-Step Solution

Answer

a. \(Moles_{Pb} ≈ 5.40 \times 10^{-4}\) moles b. \(Moles_{C6H12O6} ≈ 8.24\) moles c. \(Moles_{NaOH} ≈ 0.259\) moles d. \(Moles_{Cu^{2+}} ≈ 20.8\) moles

Step 1: a. Determine the number of moles in lead atoms

Given: \(3.25 \times 10^{20}\) atoms of lead To find the moles of lead atoms, divide the total number of atoms by Avogadro's number: \(Moles_{Pb} = \frac{3.25 \times 10^{20}}{6.022 \times 10^{23}}\) \(Moles_{Pb} ≈ 5.40 \times 10^{-4}\)

Step 2: b. Determine the number of moles in glucose molecules

Given: \(4.96 \times 10^{24}\) molecules of glucose To find the moles of glucose molecules, divide the total number of molecules by Avogadro's number: \(Moles_{C6H12O6} = \frac{4.96 \times 10^{24}}{6.022 \times 10^{23}}\) \(Moles_{C6H12O6} ≈ 8.24\)

Step 3: c. Determine the number of moles in sodium hydroxide formula units

Given: \(1.56 \times 10^{23}\) formula units of sodium hydroxide To find the moles of sodium hydroxide formula units, divide the total number of formula units by Avogadro's number: \(Moles_{NaOH} = \frac{1.56 \times 10^{23}}{6.022 \times 10^{23}}\) \(Moles_{NaOH} ≈ 0.259\)

Step 4: d. Determine the number of moles in copper (II) ions

Given: \(1.25 \times 10^{25}\) copper (II) ions To find the moles of copper (II) ions, divide the total number of ions by Avogadro's number: \(Moles_{Cu^{2+}} = \frac{1.25 \times 10^{25}}{6.022 \times 10^{23}}\) \(Moles_{Cu^{2+}} ≈ 20.8\)

Key Concepts

Avogadro's number

Avogadro's number, often denoted as \(6.022 \times 10^{23}\), is one of the fundamental constants in chemistry and signifies the number of units such as atoms, molecules, or ions in one mole of a substance. This number isn't arbitrary; it's derived from the number of carbon atoms in exactly 12 grams of pure carbon-12, and it provides a bridge between the microscopic world of atoms and the macroscopic world we experience every day.

Understanding Avogadro’s number is crucial, and to put it simply, think of it as a 'chemist's dozen' - where instead of 12 items, there are \(6.022 \times 10^{23}\) items in one group. Just as it's convenient to buy eggs by the dozen because we get an exact number of eggs, chemists use Avogadro's number so they can work with an exact number of atoms or molecules in their calculations.

When solving problems related to the number of particles in a substance, as shown in our exercise, you divide the given number of particles by Avogadro's number to find out how many moles of that substance you have. It serves as a counting unit, much like a dozen, but for atoms and molecules - critical in ensuring accurate measurement and reaction scaling in chemical equations.

Chemical Formula Units

Chemical formula units refer to the group of ions or atoms represented by a formula for an ionic compound. For example, in the compound sodium chloride (table salt), the formula unit is NaCl, indicating one sodium ion bonded to one chloride ion.

In the context of our exercise, the term 'formula units' are used for sodium hydroxide, NaOH, representing one sodium ion (Na⁺), one oxygen atom, and one hydrogen atom. This reflects the fixed ratio in which these atoms are present in every sample of the compound. It allows chemists to discuss quantities of ionic compounds in a clear and meaningful way, relating to the mole concept.

Each formula unit is counted as one entity when calculating moles, so if you have \(1.56 \times 10^{23}\) formula units of NaOH, you essentially have that many sets of (Na⁺ and OH⁻). Dividing this number by Avogadro's number provides the amount in moles, a necessary step for stoichiometric calculations in chemistry.

Stoichiometry

Stoichiometry is a section of chemistry that involves the calculation of reactants and products in chemical reactions. It’s based on the law of conservation of mass where matter cannot be created nor destroyed; therefore, the amount of reactants must equal the amount of products. This concept helps chemists convert from moles of one substance to moles of another, using the coefficients from balanced chemical equations to maintain the proper proportions.

For example, in a balanced equation, if 2 moles of hydrogen react with 1 mole of oxygen to produce 2 moles of water (2H₂ + O₂ → 2H₂O), the stoichiometry of the reaction tells us that twice as many moles of hydrogen are needed compared to oxygen.

With stoichiometry, you can predict the amount of product produced from a certain amount of reactant, or vice versa. In practical scenarios like in our exercise, if you know how many moles of a substance you have, you could determine how much of another substance you could produce in the reaction. It is essential for creating precise recipes in chemical manufacturing and understanding how substances interact in reactions.