Question

What are the empirical formulas of each of the following substances? (a) Ibuprofen, a headache remedy: \(75.69 \% \mathrm{C}, 15.51 \% \mathrm{O}, 8.80 \% \mathrm{H}\) (b) Magnetite, a naturally occurring magnetic mineral: \(72.36 \%\) Fe, \(27.64 \%\) O (c) Zircon, a mineral from which cubic zirconia is made: \(34.91 \%\) \(\mathrm{O}, 15.32 \% \mathrm{Si}, 49.77 \% \mathrm{Zr}\)

Short answer

Ibuprofen: \( C_7H_9O \), Magnetite: \( Fe_3O_4 \), Zircon: \( ZrSiO_4 \).

Step-by-step solution

Convert percentages to grams

Assume 100 g of each substance so that the percentages equal the mass in grams for simplicity. This gives us: (a) Ibuprofen: 75.69 g C, 15.51 g O, 8.80 g H (b) Magnetite: 72.36 g Fe, 27.64 g O (c) Zircon: 34.91 g O, 15.32 g Si, 49.77 g Zr.

Convert grams to moles

Use the molar mass of each element to convert the grams to moles.(a) Ibuprofen:- C: \( \frac{75.69 \text{ g}}{12.01 \text{ g/mol}} \approx 6.30 \text{ mol} \)- O: \( \frac{15.51 \text{ g}}{16.00 \text{ g/mol}} \approx 0.97 \text{ mol} \)- H: \( \frac{8.80 \text{ g}}{1.008 \text{ g/mol}} \approx 8.73 \text{ mol} \)(b) Magnetite:- Fe: \( \frac{72.36 \text{ g}}{55.85 \text{ g/mol}} \approx 1.30 \text{ mol} \)- O: \( \frac{27.64 \text{ g}}{16.00 \text{ g/mol}} \approx 1.73 \text{ mol} \)(c) Zircon:- O: \( \frac{34.91 \text{ g}}{16.00 \text{ g/mol}} \approx 2.18 \text{ mol} \)- Si: \( \frac{15.32 \text{ g}}{28.09 \text{ g/mol}} \approx 0.545 \text{ mol} \)- Zr: \( \frac{49.77 \text{ g}}{91.22 \text{ g/mol}} \approx 0.545 \text{ mol} \)

Divide by the smallest number of moles

Find the smallest number of moles calculated for each substance and divide all mole amounts by this number to find the empirical formula ratio.(a) Ibuprofen:- Ratio C: \( \frac{6.30}{0.97} \approx 6.49 \)- Ratio O: \( \frac{0.97}{0.97} = 1 \)- Ratio H: \( \frac{8.73}{0.97} \approx 9.00 \)- Empirical formula: Approximating C to the nearest whole number gives \( C_7O_1H_9 \).(b) Magnetite:- Ratio Fe: \( \frac{1.30}{1.30} = 1 \)- Ratio O: \( \frac{1.73}{1.30} \approx 1.33 \)- Empirical formula: Approximating to the nearest convenient ratio for whole numbers gives \( Fe_3O_4 \).(c) Zircon:- Ratio O: \( \frac{2.18}{0.545} \approx 4.00 \)- Ratio Si: \( \frac{0.545}{0.545} = 1 \)- Ratio Zr: \( \frac{0.545}{0.545} = 1 \)- Empirical formula: \( ZrSiO_4 \).

Write the empirical formulas

Summarize the empirical formulas for each compound based on the calculations:(a) Ibuprofen: \( C_7H_9O \)(b) Magnetite: \( Fe_3O_4 \)(c) Zircon: \( ZrSiO_4 \).

Key concepts

Percentage Composition

Percentage composition is a vital concept in chemistry. It involves expressing the proportions of each element in a compound as a percentage of the total mass.
Let's break it down:

• To find the percentage composition of an element, you calculate the mass of that specific element in a sample divided by the total mass and then multiply by 100.
• Using this concept, we can analyze mixtures and decide composition based on elements present.
• For this exercise, percentages were easily converted to mass by assuming a 100 gram sample, so 75.69% C translates to 75.69 g of C.

Understanding percentage composition is key when determining empirical formulas. It simplifies complex mixtures into understandable and manageable numbers.

Molar Mass

Molar mass is critical for converting grams of a substance to moles, a fundamental step in finding empirical formulas.
Here's what you need to know:

• Molar mass is defined as the mass of one mole of a given element or compound and is expressed in g/mol.
• For elements, it is approximately equal to the element's atomic weight found on the periodic table. For carbon in our example, it is 12.01 g/mol.
• It helps bridge the gap between the number of atoms/molecules and the measurable mass of an element or compound.

By using molar mass, we translate the percentage composition from mass in grams to moles, the smallest fundamental unit in chemistry.

Chemical Formulas

Chemical formulas convey exact proportions of elements in compounds. They come in two forms: molecular and empirical.
Empirical formulas provide the simplest positive integer ratios of atoms in a compound.

• They do not necessarily represent actual numbers of atoms in the molecule, but rather the simplest ratio.
• In this exercise, computed empirical formulas were derived based on mole ratios from mass per element.
• For example, Ibuprofen's empirical formula is derived from C, H, and O's mole ratios leading to \( C_7H_9O \).

Understanding and deriving these formulas is critical for chemists working with elemental analysis.

Mole Ratio Calculation

One of the systematic steps in finding empirical formulas is calculating mole ratios. This involves dividing the number of moles of each element by the smallest number of moles present.
Here's how:

• Once you have the number of moles for each element, identify the smallest value.
• Divide every mole value by this smallest number to get ratios for each element.
• These ratios represent the simplest whole number relation between atoms in the empirical formula.

For instance, zircon had an equal mole amount for Si and Zr, simplifying calculations to reveal its whole number ratio. Calculating accurate mole ratios ensures precise empirical formula identification, essential in chemical analysis.