Question

A compound contains 6.0 g of carbon and 1.0 g of hydrogen, and has a molar mass of 42.0 g/mol. What are the compound’s percent composition, empirical formula, and molecular formula?

Short answer

The compound's percent composition is approximately 85.7% carbon and 14.3% hydrogen. The empirical formula is CH2, and the molecular formula is C3H6.

Step-by-step solution

Calculate the moles of carbon and hydrogen.

First, let's find the number of moles of carbon (C) and hydrogen (H) in the compound. Moles of \(C=\frac{mass}{molar \thinspace mass}\) Moles of \(C=\frac{6.0 \thinspace g}{12.01 \thinspace g/mol}=0.5 \thinspace mol\) Moles of \(H=\frac{mass}{molar \thinspace mass}\) Moles of \(H=\frac{1.0 \thinspace g}{1.008 \thinspace g/mol}\approx0.994 \thinspace mol\)

Find the percent composition.

To find the percent composition, we can use the following formula: Percent composition = \(\frac{mass \thinspace of \thinspace element}{total \thinspace mass} * 100\%\) Total mass of compound = 6.0 g (C) + 1.0 g (H) = 7.0 g Percent composition of carbon (C) = \(\frac{6.0 \thinspace g}{7.0 \thinspace g} * 100\% \approx 85.7\%\) Percent composition of hydrogen (H) = \(\frac{1.0 \thinspace g}{7.0 \thinspace g} * 100\% \approx 14.3\%\)

Calculate the empirical formula.

Now let's find the empirical formula by dividing the moles of each element by the lowest mole value: Ratio of moles of C : H = \(\frac{0.5}{0.5} : \frac{0.994}{0.5} \approx 1:2\) Thus, the empirical formula is CH2.

Determine the molecular formula.

Now that we have the empirical formula, we can find the molecular formula using the given molar mass (42.0 g/mol). Molar mass of the empirical formula (CH2) = 12.01 g/mol (C) + 1.008 g/mol x 2 (H) ≈ 14.03 g/mol To find the molecular formula, we need to find the multiple of the empirical formula that matches the given molar mass: Multiple = \(\frac{molar \thinspace mass \thinspace of \thinspace compound}{molar \thinspace mass \thinspace of \thinspace empirical \thinspace formula}\) Multiple = \(\frac{42.0 \thinspace g/mol}{14.03 \thinspace g/mol} \approx 3\) Therefore, the molecular formula is 3 times the empirical formula: Molecular formula = (CH2)3 = C3H6

Key concepts

Understanding Percent Composition

Percent composition is a simple but powerful concept in chemistry that helps us understand the makeup of a compound. It tells us how much of each element is present in a compound by weight. To calculate the percent composition, you use the formula:

\[\text{Percent composition} = \left(\frac{\text{mass of element}}{\text{total mass of compound}}\right) \times 100\%\]
For example, if a compound consists of 6.0 grams of carbon (C) and 1.0 gram of hydrogen (H), and the total mass of the compound is 7.0 grams, you can calculate the percent composition for each element:

• Percent composition of carbon: \(\frac{6.0}{7.0} \times 100\% \approx 85.7\%\)
• Percent composition of hydrogen: \(\frac{1.0}{7.0} \times 100\% \approx 14.3\%\)

These percentages tell us that out of the total mass, 85.7% is carbon and 14.3% is hydrogen. This is very useful for determining how a compound might behave or react with other substances.

Determining the Empirical Formula

The empirical formula of a compound provides the simplest whole-number ratio of atoms of each element in the compound. Finding this involves a step-by-step process, primarily using the number of moles of each element.
The steps are as follows:

• Calculate the moles of each element in the compound using: \(\text{Moles of element} = \frac{\text{mass}}{\text{molar mass}}\)
• Find the smallest mole value among the elements and divide all mole values by this smallest number to get a ratio.

For instance, with 6.0 grams of carbon and 1.0 gram of hydrogen, the moles are:

• Moles of C: \(\frac{6.0 \, \text{g}}{12.01 \, \text{g/mol}} = 0.5 \, \text{mol}\)
• Moles of H: \(\frac{1.0 \, \text{g}}{1.008 \, \text{g/mol}} \approx 0.994 \, \text{mol}\)

Divide these by the smallest number (0.5 in this case) to get a ratio of 1:2, leading us to the empirical formula \(\text{CH}_2\). This formula indicates that for every atom of carbon, there are two atoms of hydrogen.

How to Perform Moles Calculation

Calculating moles is a fundamental skill in chemistry that relates the mass of a substance to the amount of substance measured in moles. The formula used is:
\[\text{Moles} = \frac{\text{mass}}{\text{molar mass}}\]
This calculation helps chemists convert a measured mass in labs to a number of moles, which is crucial for keeping chemical equations balanced and predicting the outcomes of reactions.
For example, if you have 6.0 grams of carbon and need to find out how many moles this represents:

• Carbon has a molar mass of 12.01 g/mol.
• Thus, moles of carbon = \(\frac{6.0}{12.01} = 0.5\, \text{mol}\).

Similarly, for 1.0 gram of hydrogen, with a molar mass of 1.008 g/mol, the moles of hydrogen are:

• Moles of hydrogen = \(\frac{1.0}{1.008} \approx 0.994\, \text{mol}\).

Accurately knowing these quantities helps to form and verify the empirical and molecular formulas of the compound.