Problem 39 - Chemistry Matter and Change

Question

Write the chemical formula for potassium permanganate, and then calculate the mass in grams of 2.55 mol of the compound.

Step-by-Step Solution

Answer

The mass of 2.55 mol of potassium permanganate (\( KMnO_4 \)) is 402.00 grams.

Step 1: Identify the Chemical Formula

Potassium permanganate is composed of potassium (K), manganese (Mn), and oxygen (O). The chemical formula for potassium permanganate is written as \( KMnO_4 \). This structure represents one potassium ion (K) and the permanganate ion (MnO_4).

Step 2: Determine the Molar Mass

To find the mass of 2.55 mol of \( KMnO_4 \), first calculate its molar mass. The molar mass is determined by summing the atomic masses of all the atoms in the formula. Potassium (K) has a molar mass of \( 39.10 \text{ g/mol} \), manganese (Mn) is \( 54.94 \text{ g/mol} \), and oxygen (O) is \( 16.00 \text{ g/mol} \). The molar mass of potassium permanganate is calculated as follows: \[ 1(39.10) + 1(54.94) + 4(16.00) = 158.04 \text{ g/mol} \].

Step 3: Calculate the Mass of the Compound

Now that we know the molar mass of \( KMnO_4 \) is \( 158.04 \text{ g/mol} \), calculate the mass of 2.55 moles by multiplying the number of moles by the molar mass: \[ 2.55 \text{ mol} \times 158.04 \text{ g/mol} = 402.002 \text{ g} \]. Therefore, the mass of 2.55 mol of potassium permanganate is approximately \( 402.00 \text{ g} \).

Key Concepts

Molar Mass

The concept of molar mass is crucial in chemistry. It tells us the mass of one mole of a chemical substance.
It's usually expressed in grams per mole ( ext{g/mol} ).
To find molar mass, you sum up the atomic masses of all atoms present in a molecule.
For example, in potassium permanganate (KMnO_4 ), you'll need to add together the atomic masses of potassium ( K ), manganese ( Mn ), and oxygen ( O ). This calculation is essential for converting moles to grams, which you'll often need to do in chemical analysis or reactions.

• Potassium: 39.10 g/mol
• Manganese: 54.94 g/mol
• Oxygen: 16.00 g/mol (for each of the four atoms)

When you add these up for potassium permanganate, it totals to 158.04 g/mol.

Potassium Permanganate

Potassium permanganate is a chemical compound with the formula KMnO_4 .
This compound is a powerful oxidizing agent and is often used in chemistry as a disinfectant and in water treatment.
The permanganate ion (MnO_4^{-} ) is what gives it its distinctive purple color.
Potassium permanganate reacts with many organic substances and reduces easily to MnO_2 , proving useful in different oxidation reactions.

• Color: Typically purple in aqueous solutions.
• Common Uses:
  • Oxidation reactions in chemical syntheses.
  • As a disinfectant to kill bacteria.
  • Water purification processes.

Understanding its chemical formula, KMnO_4 , is crucial for solving stoichiometry problems, especially when calculating mass.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions using a balanced equation.
The calculations rely heavily on the concept of moles and the molar masses of substances.
When you're determining how much of a chemical you need or how much will be produced, stoichiometry is the tool you use.
In our example, we calculated the mass of potassium permanganate by multiplying its moles (2.55) by its molar mass (158.04 ext{g/mol} ).

• Purpose: Determine the proportions of substances involved in chemical reactions.
• Helps to understand the quantities of each reactant needed and products formed.
• Ties together concepts of moles, molar mass, and chemical equations.

Without stoichiometry, predicting or measuring exact amounts of chemicals in reactions would be quite difficult.

Chemical Formulas

Chemical formulas provide a shorthand way to represent a chemical compound.
Each formula indicates the kind and number of atoms present in the compound.
For example, KMnO_4 tells us there is one potassium atom, one manganese atom, and four oxygen atoms per molecule.
These formulas are vital for communicating information about chemical reactions and components.

• Types of Formulas:
  • Empirical: Shows the simplest whole-number ratio of elements.
  • Molecular: Displays the actual number of each type of atom in a molecule.
  • Structural: Provides insight into the arrangement of atoms in a molecule.
• Purpose: Quickly convey the structure and composition of compounds.

In practical chemistry, this helps to identify the make-up of substances you are working with in an experiment or calculation.