Problem 83 - Chemistry An Atoms First Approach

Question

A compound that contains only carbon, hydrogen, and oxygen is \(48.64 \%\) C and \(8.16 \%\) H by mass. What is the empirical formula of this substance?

Step-by-Step Solution

Answer

The empirical formula of the substance is \(C_1H_2O_1\), which can be simplified to \(CHO\).

Step 1: Calculate the percentage of oxygen atoms

We are given the percentage by mass for carbon and hydrogen. Since the compound contains only carbon, hydrogen, and oxygen, we can calculate the percentage of oxygen by subtracting the sum of carbon and hydrogen percentages from 100%: Percentage of oxygen = 100% - (48.64% C + 8.16% H) Now, plug in the given percentages and compute the percentage of oxygen.

Step 2: Convert the percentages to moles

To find the ratio of moles of carbon (C), hydrogen (H), and oxygen (O), we must convert the percentages of each element into moles. We can do this by dividing the percentages by the respective atomic masses of the elements. - Atomic mass of C = 12.01 g/mol - Atomic mass of H = 1.008 g/mol - Atomic mass of O = 16.00 g/mol Moles of C = (48.64% / 12.01 g/mol) = x mol Moles of H = (8.16% / 1.008 g/mol) = y mol Moles of O = (z% / 16.00 g/mol) = w mol

Step 3: Find the ratio of moles of each element

Now, we have to find the ratio x:y:w (moles of C: moles of H: moles of O). To do this, divide each mole value by the smallest mole value obtained in step 2. Then, round the ratios to the nearest whole number.

Step 4: Write the empirical formula

Based on the ratio x:y:w determined in step 3, find the empirical formula of the compound by writing the elements with their whole-number ratios as subscripts in the formula. The final result will give the simplest formula (empirical formula) for the compound.

Key Concepts

Molecular Composition

Understanding the molecular composition of a compound involves knowing the elements present and their respective proportions by mass. In our exercise, the compound consists of carbon, hydrogen, and oxygen. To find which elements and how much of each are in the compound, you start by identifying the given mass percentages. These percentages tell you how much of each element is present in a specific portion of the compound.

• Carbon is given as 48.64% of the compound.
• Hydrogen constitutes 8.16% by mass.
• Oxygen is not provided directly, but can be calculated by subtracting the sum of the percentages of carbon and hydrogen from 100%.

Once you have the percentages for each element, these values can be used to further analyze the compound in terms of their atomic contributions, helping to derive other quantities like moles.

Percent Composition

Percent composition is a key concept in determining the makeup of a compound, especially when translating known mass percentages into empirical formulas. The percent composition tells you what fraction of the total mass of a compound is due to each element present. To calculate this:

• Sum all given element percentages.
• Subtract from 100% to find any missing component, as was done to derive oxygen's percentage.

Here, oxygen's percentage is calculated as:
Percentage of oxygen = 100% - (48.64% C + 8.16% H) = 43.20%.
The percent composition aids in transforming these values from percentages into moles to find empirical formulas, ensuring you know how much each element contributes to the compound's mass.

Mole Ratio Calculation

Mole ratio calculation is essential in determining the simplest whole-number ratio of elements in a compound, known as the empirical formula. Once you have the percentages of the elements, convert these into moles by using the atomic masses:

• Carbon: Divide 48.64% by 12.01 g/mol (molar mass of carbon).
• Hydrogen: Divide 8.16% by 1.008 g/mol (molar mass of hydrogen).
• Oxygen: Divide 43.20% by 16.00 g/mol (molar mass of oxygen).

After performing these calculations, you get the number of moles for each element. The next step is to obtain the simplest ratio by dividing each mole value by the smallest one calculated.
Rounding these results yields whole numbers needed to develop the empirical formula. This process ensures you interpret the chemical composition accurately in terms of moles, leading you to understand the fundamental structure of the compound.