Question

A compound with a formula mass of 42.08 u is found to be 85.64% carbon and 14.36% hydrogen by mass. Find its molecular formula.

Short answer

The molecular formula is C3H6.

Step-by-step solution

Identify the elements involved

The compound contains carbon (C) and hydrogen (H) as given by the mass percentages.

Convert mass percentages to grams

Assume a 100 g sample of the compound. This means there would be 85.64 g of carbon and 14.36 g of hydrogen.

Convert grams to moles

Use the molar masses to convert grams to moles. The molar mass of carbon is 12.01 g/mol and for hydrogen, it is 1.008 g/mol.

Calculate moles of each element

For Carbon: \( \text{Moles of } C = \frac{85.64 \text{ g}}{12.01 \text{ g/mol}} = 7.13 \text{ moles} \) For Hydrogen: \( \text{Moles of } H = \frac{14.36 \text{ g}}{1.008 \text{ g/mol}} = 14.25 \text{ moles} \)

Determine the simplest molar ratio

Divide each element’s mole quantity by the smallest number of moles calculated. For Carbon: \( \frac{7.13}{7.13} = 1 \) For Hydrogen: \( \frac{14.25}{7.13} \text{ is approximately } 2 \) Thus, the ratio C:H is 1:2.

Write the empirical formula

The empirical formula is determined from the molar ratio: CH2.

Calculate the empirical formula mass

The empirical formula mass for CH2 is calculated as follows: \( 12.01 \text{ (for C)} + 2 \times 1.008 \text{ (for 2 H)} = 14.026 \text{ u} \)

Determine the number of empirical units in molecular formula

Divide the compound's formula mass by the empirical formula mass: \( \frac{42.08 \text{ u}}{14.026 \text{ u}} \text{ is approximately } 3 \). Hence, there are 3 empirical units in the molecular formula.

Write the molecular formula

Multiply the empirical formula by the number of empirical units: \( (CH2)_3 \text{ or } C3H6 \) is the molecular formula.

Key concepts

Empirical Formula

Understanding the empirical formula is essential for molecular formula determination. It represents the simplest whole-number ratio of elements in a compound. To find the empirical formula, here are the steps:

1. **Identify Elements and Their Percentages**: Our problem involves carbon (C) and hydrogen (H) with mass percentages of 85.64% and 14.36%, respectively.
2. **Convert Percentages to Grams**: Assuming a 100 g sample, this translates to 85.64 g of carbon and 14.36 g of hydrogen.
3. **Convert to Moles**: Use the molar masses (Carbon: 12.01 g/mol, Hydrogen: 1.008 g/mol) to determine the moles:

• For Carbon: \( \frac{85.64 \text{ g}}{12.01 \text{ g/mol}} = 7.13 \text{ moles} \)
• For Hydrogen: \( \frac{14.36 \text{ g}}{1.008 \text{ g/mol}} = 14.25 \text{ moles} \)

4. **Determine Simple Ratio**: Divide by the smallest mole value to simplify the ratio:

• Carbon: \( \frac{7.13}{7.13} = 1 \)
• Hydrogen: \( \frac{14.25}{7.13} \text{ is approximately } 2 \)

The ratio of C:H is 1:2; thus, the empirical formula is CH2. Understanding these ratios and calculations ensures that you're adept at finding empirical formulas.

Molar Mass Calculation

The molar mass is the mass of one mole of a substance. It's crucial for converting grams to moles and vice versa. Here's how to calculate it:

1. **Identify Elemental Masses**: Use the periodic table for precise atomic masses. For example, Carbon (C) = 12.01 g/mol, Hydrogen (H) = 1.008 g/mol.
2. **Sum the Atomic Masses**: If the empirical formula is known (CH2 in our case), add the mass of each atom:

• For CH2: \(12.01 \text{ (for C)} + 2 \times 1.008 \text{ (for H)} = 14.026 \text{ u} \)

This gives the molar mass for CH2.

Knowing the molar mass helps in identifying the actual molecular formula from the empirical formula by correlating with the given formula mass.

Molecular Formula

Once the empirical formula and its mass are known, determining the molecular formula involves a few more steps:

1. **Given Information**: Use the provided formula mass (in this case, 42.08 u) and empirical formula mass (14.026 u for CH2).
2. **Calculate Units**: Find the ratio between the molecular formula mass and empirical formula mass:

• \( \frac{42.08 \text{ u}}{14.026 \text{ u}} \text{ is approximately } 3 \)

This indicates that the molecular formula contains 3 empirical units.
3. **Write Molecular Formula**: Multiply the empirical formula (CH2) by the number of units to get the molecular formula: \( (CH2)_3 \text{ or C3H6} \).
Determining the molecular formula helps in accruing the exact composition and molecular weight of complex molecules.