Question

For \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\), which is the correct mole relationship? (a) \(9 \times\) mole of \(\mathrm{Cu}=\) mole of \(\mathrm{O}\) (b) \(5 \times\) mole of \(\mathrm{Cu}=\) mole of \(\mathrm{O}\) (c) \(9 \times\) mole of \(\mathrm{Cu}=\) mole of \(\mathrm{O}_{2}\) (d) mole of \(\mathrm{Cu}=5 \times \mathrm{mole}\) of \(\mathrm{O}\)

Short answer

The correct mole relationship is (a) 9 times mole of Cu equals to mole of O.

Step-by-step solution

Identify the chemical formula

Look at the provided chemical formula for Copper(II) sulfate pentahydrate, which is \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\). This gives the number of atoms of each element in one molecule of the compound.

Count the atoms of Copper (Cu) and Oxygen (O)

In one molecule of the compound, there is 1 atom of Copper (Cu) and 4 atoms of Oxygen (O) in the sulfate ion (\(\mathrm{SO}_{4}^{2-}\)) plus an additional 5 molecules of water, each containing 1 Oxygen atom, totaling to 9 Oxygen atoms.

Establish the mole relationship between Cu and O

Since there is 1 mole of Cu and a total of 9 moles of O (from both the sulfate ion and the water molecules), the correct mole relationship is that 1 mole of Cu corresponds to 9 moles of Oxygen.

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that quantitatively relates the amounts of substances involved in chemical reactions. It's based on the conservation of mass and the principle that the same number of atoms that react to form products must have been present in the reactants.

Consider a simple analogy: if you're baking a cake, the recipe might require 2 eggs for every cup of flour. Stoichiometry in chemistry follows a similar logic; it helps us understand the 'recipe' for a chemical reaction. For instance, if you start with 2 moles of hydrogen gas (H2) to react with 1 mole of oxygen gas (O2) to form water (H2O), stoichiometry will tell you that the reaction produces 2 moles of water.

Stoichiometric calculations require a balanced chemical equation, from which the mole ratio of reactants and products can be derived. This ratio enables chemists to predict how much of each substance is needed or produced in a reaction. Understanding stoichiometry is crucial for solving mole relationship problems, where the goal is to determine the mole ratio between two or more substances in a compound or reaction.

Chemical Formula

The chemical formula of a compound tells us the exact number of different atoms of each element that make up the smallest unit of that compound. In the case of Copper(II) sulfate pentahydrate, represented by \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\), the formula indicates that one unit of this compound consists of one Copper atom (Cu), one Sulfate ion (\(\mathrm{SO}_{4}^{2-}\)) which includes four Oxygen atoms (O), and five water molecules (\(5 \mathrm{H}_{2} \mathrm{O}\)) each containing two Hydrogen atoms (H) and one Oxygen atom.

The chemical formula is pivotal because it serves as a blueprint for the compound's structure and composition. This is essential for understanding and solving problems related to the mole concept, as it allows us to count the number of atoms of each element in the compound and therefore match the mole relationships accurately. In our exercise, it was the identification and interpretation of the chemical formula that led to the correct answer—illustrating the direct relationship between one mole of Cu and nine moles of O.

Atoms and Moles

Atoms are the smallest units of matter that retain the identity of an element. While working with atoms in chemical reactions, we use the mole, which is a unit that allows chemists to count atoms in terms they can measure.

A mole corresponds to Avogadro's number (approximately \(6.022 \times 10^{23}\)) of particles, which can be atoms, molecules, ions, or electrons. It's similar to a 'dozen' representing 12 items, but in this case, a mole represents a much larger and standardized quantity. This vast number is used because atoms and molecules are incredibly small and cannot be counted individually for practical laboratory purposes.

In mole relationship problems like the one in our exercise, knowing that there is one mole of Cu is not enough. We need to consider the entire compound to conclude that this one mole of Cu corresponds to nine moles of O, due to the additional five water molecules attached to the sulfate ion. Understanding the relationship between atoms and moles is fundamental in translating the microscopic world of atoms into quantities that can be empirically and practically used in scientific calculations.