Question

Determine the empirical formulas of the compounds with the following compositions: (a) 40.1 percent \(\mathrm{C}\), 6.6 percent \(\mathrm{H}, 53.3\) percent \(\mathrm{O} ;\) (b) 18.4 percent \(\mathrm{C}\), 21.5 percent \(\mathrm{N}, 60.1\) percent \(\mathrm{K}\)

Short answer

Compound (a): \( \text{CH}_2\text{O} \); Compound (b): \( \text{CNK} \).

Step-by-step solution

Convert Percentages to Grams

Assume you have 100 g of each compound. This means you have 40.1 g of C, 6.6 g of H, and 53.3 g of O for compound (a); 18.4 g of C, 21.5 g of N, and 60.1 g of K for compound (b).

Convert Grams to Moles

For compound (a), calculate moles of each element:- For C: \( \frac{40.1 \text{ g}}{12.01 \text{ g/mol}} = 3.34 \text{ mol} \)- For H: \( \frac{6.6 \text{ g}}{1.01 \text{ g/mol}} = 6.53 \text{ mol} \)- For O: \( \frac{53.3 \text{ g}}{16.00 \text{ g/mol}} = 3.33 \text{ mol} \)For compound (b), calculate moles of each element:- For C: \( \frac{18.4 \text{ g}}{12.01 \text{ g/mol}} = 1.53 \text{ mol} \)- For N: \( \frac{21.5 \text{ g}}{14.01 \text{ g/mol}} = 1.54 \text{ mol} \)- For K: \( \frac{60.1 \text{ g}}{39.10 \text{ g/mol}} = 1.54 \text{ mol} \)

Determine the Mole Ratio

For each compound, calculate the mole ratio by dividing each amount of moles by the smallest value of moles computed:For compound (a):- C: \( \frac{3.34}{3.33} = 1.00 \)- H: \( \frac{6.53}{3.33} = 1.96 \)- O: \( \frac{3.33}{3.33} = 1.00 \)For compound (b):- C: \( \frac{1.53}{1.53} = 1.00 \)- N: \( \frac{1.54}{1.53} = 1.01 \)- K: \( \frac{1.54}{1.53} = 1.01 \)

Write the Empirical Formula

For compound (a), round the numbers to the nearest whole number:- C: 1, H: 2, O: 1 leading to the empirical formula \( \text{CH}_2\text{O} \).For compound (b), round the numbers to the nearest whole number:- C: 1, N: 1, K: 1 leading to the empirical formula \( \text{CNK} \).

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves the calculation of reactants and products in chemical reactions. It is based on the law of conservation of mass, where matter cannot be created or destroyed in an isolated system. In the context of determining empirical formulas, stoichiometry helps us understand the quantitative relationship between the different elements in a compound.

The process generally involves:

• Knowing the percent composition of a compound
• Converting these percentages to masses (assuming a baseline of 100 grams)
• Converting those masses to moles, using the molar mass of each element
• Finding the simplest whole-number ratio of moles of each element present

This systematic approach allows us to write a chemical formula that represents the simplest ratio of the atoms in a compound. By adhering to stoichiometry, we ensure that our calculations are grounded in the principles of chemical reactions and compositions, making it an essential skill in chemistry.

Mole Calculation

Mole calculation is a key component in stoichiometry and chemistry as a whole. It involves using the mole concept to relate a given mass of a substance to the number of entities (like atoms or molecules) it contains. The mole is a bridge between the atomic scale and the macroscopic scale of laboratory chemistry.

To perform mole calculations, follow these guidelines:

• Determine the molar mass of each element, which you can find on the periodic table expressed in g/mol
• Convert the mass of each element in a given problem to moles by dividing the mass by the element's molar mass
• Use these mole values to find the smallest whole-number ratio when determining empirical formulas

The equation used is:\(\text{Moles of } A = \frac{\text{Mass of } A}{\text{Molar Mass of } A}\)This calculation gives you a quantitative understanding of how much of a substance you're working with, which is crucial for predicting the amount of products in chemical reactions.

Elemental Composition

Understanding elemental composition is critical when determining the empirical formula of a compound. Elemental composition tells you the percentage by mass of each element in a compound, providing valuable insight into its structure and properties.

During calculations:

• Start by assuming you have a 100g sample of the compound. This makes it easy to convert percentage data into grams.
• Use these masses to calculate moles of each element.
• From here, convert these values to the simplest whole-number ratio to find the empirical formula.

Elemental composition not only helps in deducing the empirical formula, but also plays a role when you're advancing toward understanding molecular formulas and reaction stoichiometry. By mastering these concepts, students can accurately describe the composition of compounds, essential for deeper chemical analysis and synthesis.