Problem 124 - Chemistry Matter and Change

Question

Insect Repellent Many insect repellents use DEET as the active ingredient. DEET was patented in 1946 and is effective against many biting insects. What must you know to determine the molar mass of DEET?

Step-by-Step Solution

Answer

To determine the molar mass of DEET, you need to know its chemical formula, which is C12H17NO. Then, multiply the atomic mass of each element by the number of its atoms present in one molecule of DEET and add up the products. The molar mass of DEET is \(191.30\, u\).

Step 1: Find the chemical formula of DEET

We need to know the chemical formula of DEET to calculate its molar mass. The chemical formula of DEET is C12H17NO.

Step 2: Identify the elements and their atomic masses

Now that we know the chemical formula of DEET, we can identify the elements it contains: Carbon (C), Hydrogen (H), Nitrogen (N), and Oxygen (O). We also need to know their respective atomic masses. - The atomic mass of Carbon (C) = \(12.01\, u\) - The atomic mass of Hydrogen (H) = \(1.01\, u\) - The atomic mass of Nitrogen (N) = \(14.01\, u\) - The atomic mass of Oxygen (O) = \(16.00\, u\)

Step 3: Calculate the molar mass of DEET

To calculate the molar mass of DEET, we need to multiply the atomic mass of each element by the number of its atoms present in one molecule of DEET and then add up these products. Molar mass of DEET = (Number of Carbon atoms × Atomic mass of Carbon) + (Number of Hydrogen atoms × Atomic mass of Hydrogen) + (Number of Nitrogen atoms × Atomic mass of Nitrogen) + (Number of Oxygen atoms × Atomic mass of Oxygen) Molar mass of DEET = \((12 \times 12.01\, u) + (17 \times 1.01\, u) + (1 \times 14.01\, u) + (1 \times 16.00\, u)\) Molar mass of DEET = \(144.12\, u + 17.17\, u + 14.01\, u + 16.00\, u\) Molar mass of DEET = \(191.30\, u\) So, the molar mass of DEET is \(191.30\, u\).

Key Concepts

Chemical Formula

When determining the molar mass of a compound, the first step is to know its chemical formula. A chemical formula tells us how many of each type of atom are present in a single molecule of a substance. Knowing this helps us see exactly what elements make up the compound.

For example, DEET, a common insect repellent, has a chemical formula of \( \text{C}_{12}\text{H}_{17}\text{NO} \). This formula indicates that one molecule of DEET contains:

• 12 carbon atoms
• 17 hydrogen atoms
• 1 nitrogen atom
• 1 oxygen atom

Each of these numbers after the element symbols tells you how many atoms of each element there are in the molecule. Grasping this helps in calculating the molar mass accurately.

Atomic Mass

Once we have the chemical formula, we need to focus on the atomic mass of the elements involved. Atomic mass is essentially the weight of an atom expressed in atomic mass units (u). It is crucial for calculating molar mass, as it allows us to sum up the total weight of the atoms in a compound.

In the case of DEET:

• Carbon (C) has an atomic mass of \( 12.01\, u \)
• Hydrogen (H) has an atomic mass of \( 1.01\, u \)
• Nitrogen (N) has an atomic mass of \( 14.01\, u \)
• Oxygen (O) has an atomic mass of \( 16.00\, u \)

These values are typically found on the periodic table under each element symbol. Multiplying the atomic mass by the number of atoms, and summing these products, gives a compound's precise molar mass.

Chemical Elements

Chemical elements are the building blocks of all compounds. Understanding these basic units helps us comprehend more complex chemical concepts.

Each element is unique and has specific properties such as

• Atomic number, which reflects the number of protons in its nucleus
• Symbol, a one or two-letter abbreviation often derived from its name
• Atomic mass, which tells us its weight when accounting for isotopes

In DEET, we deal with four chemical elements: carbon, hydrogen, nitrogen, and oxygen. These elements combine in specific ratios to form the compound DEET. By knowing their properties, particularly atomic mass, we can calculate the molar mass often needed for chemical calculations, such as reactions and formulations. This foundational knowledge is essential in the field of chemistry.