Question

What is the simplest formula of a compound that is composed of \(72.4 \%\) iron and \(27.6 \%\) oxygen by weight?

Short answer

The simplest formula for the compound composed of \(72.4\%\) iron and \(27.6\%\) oxygen by weight is Fe_3O_4.

Step-by-step solution

Convert percentages to mass

We first convert the given percentages to mass, assuming we have 100g of the compound. This makes it easy to work with the percentages directly as mass: - Iron: \(72.4\%\) of 100g = 72.4g - Oxygen: \(27.6\%\) of 100g = 27.6g

Convert mass to moles

Next, we need to convert the mass of each element to moles. To do this, we'll use the molar mass of each element: - Iron (Fe): Molar mass = 55.845 g/mol - Oxygen (O): Molar mass = 16 g/mol The moles of each element can be calculated by dividing the mass by the molar mass: - Moles of Iron: \(\frac{72.4\,\text{g}}{55.845\,\text{g/mol}} \approx 1.296\,\text{mol}\) - Moles of Oxygen: \(\frac{27.6\,\text{g}}{16\,\text{g/mol}} = 1.725\,\text{mol}\)

Find the mole ratio

Now that we have the moles of each element, we will find the ratio between them to determine the simplest formula. We'll divide both mole values by the smallest value (which is the moles of iron) to get the ratio: - Ratio of Iron: \(\frac{1.296\,\text{mol}}{1.296\,\text{mol}} = 1\) - Ratio of Oxygen: \(\frac{1.725\,\text{mol}}{1.296\,\text{mol}} \approx 1.331\) Since the ratio is not a whole number, we'll multiply both numbers by a small whole number in order to obtain whole number stoichiometric coefficients. In this case, multiplying both ratios by 3 gives us: - Ratio of Iron: \(1 \times 3 = 3\) - Ratio of Oxygen: \(1.331 \times 3 \approx 3.993 \approx 4\)

Write the simplest formula

Finally, we'll use the ratios obtained in step 3 to write the simplest formula for the compound: Fe_3O_4 The simplest formula for the compound composed of 72.4% iron and 27.6% oxygen by weight is Fe_3O_4.

Key concepts

Mole Calculations

Calculating moles is the foundational step in determining the simplest or empirical formula of a compound. Moles connect the mass of a substance to the number of atoms or molecules it contains. This step ensures a direct link between tangible, weighable amounts and the fundamental particles involved.
To calculate moles from mass, use the formula: \[ \text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}} \]

• Iron (Fe): Given its mass (72.4g) and molar mass (55.845 g/mol), it converts to approximately 1.296 moles.
• Oxygen (O): With its mass (27.6g) and molar mass (16 g/mol), the conversion results in 1.725 moles.

Understanding how to calculate moles is vital, as it is used extensively from chemistry labs to industrial chemical processes. Grasping this concept helps in efficiently transitioning between amounts in grams and the substance at the atomic level.

Percentage Composition

The percentage composition of a compound breaks down its ingredients by mass percentage. It's like a recipe for the compound, explaining what proportion each element contributes.
In this exercise, the compound comprises 72.4% iron and 27.6% oxygen. To simplify calculations, we can think of this as a 100g sample, which directly converts these percentages into grams: 72.4g of iron and 27.6g of oxygen.
Working with percentage composition helps chemists and students alike to conceptualize the relative amounts of each element involved in a compound. It clarifies how the bulk of one element compares to another within a compound and lays the groundwork for mole calculations and eventually deducing the simplest formula.

Stoichiometry

Stoichiometry involves quantifying the relationships and proportions between reactants and products in chemical reactions. It's the toolbox enabling chemists to determine the amount of reactants necessary or predict the amount of product that will form.
For our exercise, stoichiometry guides us to the empirical formula from percentage composition and moles. We found the ratio of moles between iron and oxygen: a ratio close to 1:1.331. Since empirical formulas require whole number ratios, we scaled this by multiplying both sides to achieve approximately 3:4.
The whole number ratio led us to Fe₃O₄, a critical conclusion that expresses the simplest relationship of atoms of the elements in the compound. Mastering stoichiometry is essential for accurately interpreting chemical equations and solving complex chemical problems.