Question

Calculate the percent by mass of the element mentioned first in the formulas for each of the following compounds. a. iron(II) sulfate b. silver(I) oxide c. strontium chloride d. vinyl acetate, \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{2}\) e. methanol, \(\mathrm{CH}_{3} \mathrm{OH}\) f. aluminum oxide g. potassium chlorite h. potassium chloride

Short answer

The percent by mass of the first element in each compound is as follows: a. Iron(II) sulfate: \(≈ 36.76\%\) Fe b. Silver(I) oxide: \(≈ 92.84\%\) Ag c. Strontium chloride: \(≈ 55.26\%\) Sr d. Vinyl acetate: \(≈ 55.84\%\) C e. Methanol: \(≈ 37.47\%\) C f. Aluminum oxide: \(≈ 52.94\%\) Al g. Potassium chlorite: \(≈ 31.89\%\) K h. Potassium chloride: \(≈ 52.44\%\) K

Step-by-step solution

Find the molecular weight of iron(II) sulfate

Iron(II) sulfate has the formula FeSO4. The molecular weight of FeSO4 is the sum of the atomic weights of each atom. Using the periodic table, we find the atomic weights as: - Iron (Fe): 55.845 u - Sulfur (S): 32.065 u - Oxygen (O): 16.00 u

Calculate the molecular weight of FeSO4

Now calculate the molecular weight of FeSO4: Molecular weight = (1 × 55.845 u) + (1 × 32.065 u) + (4 × 16.00 u) = 151.909 u

Find the percent by mass of iron (Fe)

Divide the atomic weight of Fe by the molecular weight of FeSO4 and multiply by 100%. Percent by mass of Fe = (55.845/151.909) × 100% ≈ 36.76% b. silver(I) oxide

Find the molecular weight of silver(I) oxide

Silver(I) oxide has the formula Ag2O. The molecular weight of Ag2O is the sum of the atomic weights of each atom. Using the periodic table, we find the atomic weights as: - Silver (Ag): 107.87 u - Oxygen (O): 16.00 u

Calculate the molecular weight of Ag2O

Now calculate the molecular weight of Ag2O: Molecular weight = (2 × 107.87 u) + (1 × 16.00 u) = 231.74 u

Find the percent by mass of silver (Ag)

Divide the atomic weight of Ag by the molecular weight of Ag2O and multiply by 100%. Percent by mass of Ag = (2 × 107.87/231.74) × 100% ≈ 92.84% Follow the same procedure for the remaining compounds. c. strontium chloride: Molecular weight of SrCl2: (1 × 87.62) + (2 × 35.453) = 158.526 u Percent by mass of Sr: (87.62/158.526) × 100% ≈ 55.26% d. vinyl acetate, C4H6O2: Molecular weight of C4H6O2: (4 × 12.011) + (6 × 1.008) + (2 × 16.00) = 86.082 u Percent by mass of C: (4 × 12.011/86.082) × 100% ≈ 55.84% e. methanol, CH3OH: Molecular weight of CH3OH: (1 × 12.011) + (4 × 1.008) + (1 × 16.00) = 32.042 u Percent by mass of C: (12.011/32.042) × 100% ≈ 37.47% f. aluminum oxide: Molecular weight of Al2O3: (2 × 26.982) + (3 × 16.00) = 101.964 u Percent by mass of Al: (2 × 26.982/101.964) × 100% ≈ 52.94% g. potassium chlorite: Molecular weight of KClO2: (1 × 39.098) + (1 × 35.453) + (2 × 16.00) = 122.548 u Percent by mass of K: (39.098/122.548) × 100% ≈ 31.89% h. potassium chloride: Molecular weight of KCl: (1 × 39.098) + (1 × 35.453) = 74.551 u Percent by mass of K: (39.098/74.551) × 100% ≈ 52.44%

Key concepts

Molecular Weight Calculation

Calculating molecular weight is a crucial step in finding the percent by mass of elements in a compound. To determine the molecular weight of a compound, you need to know the atomic weights of the elements that make up the compound. These atomic weights are available on the periodic table.

Here's how you do it:

• Identify the chemical formula of the compound.
• Count the number of atoms of each element present in the compound.
• Multiply the atomic weight of each element by the number of atoms of that element.
• Sum these values to get the total molecular weight.

For example, let's calculate the molecular weight of iron(II) sulfate, \( \text{FeSO}_4 \). First, find the atomic weights: Iron (Fe) is 55.845 u, Sulfur (S) is 32.065 u, and Oxygen (O) is 16 u. The calculation goes like this: \[ \text{Molecular weight of FeSO}_4 = (1 \times 55.845) + (1 \times 32.065) + (4 \times 16.00) = 151.909 \text{ u} \]

By practicing these calculations, you will better understand how each element contributes to the total weight of the compound.

Chemical Formulas

A chemical formula is a concise way of expressing information about the atoms that constitute a particular chemical compound. It provides the type and number of atoms present in a compound, which is essential for molecular weight calculations and other chemical analyses.

There are different types of chemical formulas:

• Empirical Formulas: Show the simplest whole-number ratio of atoms in a compound. For example, the empirical formula of hydrogen peroxide is \( \text{HO} \), though its molecular formula is \( \text{H}_2\text{O}_2 \).
• Molecular Formulas: Give the exact number of atoms of each element in a molecule. For instance, \( \text{C}_4\text{H}_6\text{O}_2 \) is the molecular formula for vinyl acetate.
• Structural Formulas: Illustrate the arrangement of atoms within the molecule. These are more detailed and show how atoms are bonded in a compound.

Understanding chemical formulas is fundamental to chemistry, as they convey essential details about compounds and help you perform important calculations.

Periodic Table Elements

The periodic table is an indispensable tool for chemists. It organizes all known chemical elements based on their atomic numbers, electron configurations, and recurring chemical properties. Elements are arranged in groups (columns) and periods (rows), and each element has a unique atomic number that tells you how many protons are in its nucleus.

The periodic table helps you:

• Find the atomic weight of elements, which is crucial for calculating molecular weights.
• Determine the number of valence electrons, which influences how elements bond with others.
• Predict element properties and behaviors based on their position in the table (e.g., metals, nonmetals).

Using the periodic table, you can quickly look up atomic weights for your molecular weight calculations, whether you're working with common compounds like water or complex ones like potassium chlorite \( \text{KClO}_2 \). This makes the periodic table an efficient reference for understanding the details and behaviors of different chemical substances.