Problem 111 - Chemistry Matter and Change

Question

How many atoms of each element are present in five formula units of calcium permanganate? (Chapter 7)

Step-by-Step Solution

Answer

In five formula units of calcium permanganate \((Ca(MnO_4)_2)\), there are 5 calcium atoms, 10 manganese atoms, and 40 oxygen atoms.

Step 1: Identify the chemical formula of calcium permanganate

Calcium is a group II element with a positive two (+2) charge, while permanganate is a polyatomic ion with a negative one (-1) charge and has the chemical formula \(MnO_4^{-}\). Therefore, to obtain a neutral compound, we need one Ca²⁺ ion and two permanganate ions. So, the chemical formula for calcium permanganate is \(Ca(MnO_4)_2\).

Step 2: Determine the number of atoms in one formula unit of calcium permanganate

In one formula unit of calcium permanganate \((Ca(MnO_4)_2)\), we have: - 1 atom of calcium (Ca) - 2 atoms of manganese (Mn) since there are two permanganate ions in the formula - 8 atoms of oxygen (O) since there are four oxygen atoms in each permanganate ion and there are two permanganate ions in the formula

Step 3: Calculate the number of atoms in five formula units of calcium permanganate

Now that we have the number of atoms of each element in one formula unit, let's multiply these numbers by 5 to find the number of atoms in five formula units: - Calcium atoms: \(1 \times 5 = 5\) - Manganese atoms: \(2 \times 5 = 10\) - Oxygen atoms: \(8 \times 5 = 40\) So, there are 5 calcium atoms, 10 manganese atoms, and 40 oxygen atoms in five formula units of calcium permanganate.

Key Concepts

Formula Units of Compounds

Understanding formula units of compounds is essential in the field of chemistry. A formula unit refers to the simplest whole-number ratio between the atoms, ions, or molecules in a compound. For ionic compounds, which consist of a crystal lattice, a formula unit represents the lowest ratio of ions that make up the crystal. It's a way to express the composition of the compound without implying the large number of individual ions in the solid.

For example, the formula unit of sodium chloride (table salt) is NaCl, indicating a 1:1 ratio of sodium ions to chloride ions. Calcium permanganate, with a formula of \(Ca(MnO_4)_2\), tells us that one calcium ion pairs with two permanganate ions to form the compound. When dealing with formula units, always ensure to identify the correct ionic ratio to proceed with accurate calculations and avoid common mistakes.

Counting Atoms in Chemical Formulas

Chemical formulas serve as a shorthand to convey detailed information about the composition of a compound. Learning to count atoms in chemical formulas is a foundational chemistry skill. Begin by identifying each element present and the subscript that follows it, which shows the number of atoms of that element in one molecule or formula unit. If there is no subscript, it is implied that there is just one atom of that element.

For practice, let's consider water, \(H_2O\), which tells us there are two hydrogen atoms and one oxygen atom in each molecule. If we encounter a compound like calcium permanganate, \(Ca(MnO_4)_2\), we need to pay special attention to parentheses, which imply that the subscript outside affects everything inside the parentheses. There is one calcium, two manganese, and because the subscript '4' applies to oxygen and is multiplied by '2' due to the outer subscript, there are eight oxygen atoms. It is paramount to be thorough and methodical when counting atoms to avoid calculation errors.

Stoichiometry of Compounds

Stoichiometry is the study of the quantitative relationships, or ratios, of reactants and products in chemical reactions. It is based on the conservation of mass and the concept that elements combine in fixed ratios to form compounds. Stoichiometry extends beyond simple reactions to encompass the calculations involved in determining the amounts of substances in any given compound.

Using the stoichiometric coefficients from balanced chemical equations and the molar mass of the substances involved, chemists can calculate how much of each reactant is needed and how much of each product is formed. In the context of our calcium permanganate example, if you ever need to calculate the mass of five formula units, use the compound's molar mass and Avogadro's number. This kind of conversion is crucial in laboratory settings and industrial applications where precise measurements are imperative.