Problem 90 - Introductory Chemistry Atoms First

Question

A \(2.230-\mathrm{g}\) sample of a solid is subjected to combustion analysis, yielding \(76.59 \% \mathrm{C}\) and \(6.39 \% \mathrm{H}\). It may also contain oxygen. (a) What is the empirical formula for this compound? (b) The molar mass of this compound is determined to be about \(94 \mathrm{~g} / \mathrm{mol}\). What is the molecular formula for this compound?

Step-by-Step Solution

Answer

(a) The empirical formula for the compound is C_2H_6O. (b) The molecular formula for the compound is C_4H_12O_2.

Step 1: (a) Calculate moles of each element in the sample

First, we need to convert the given percentages of carbon, hydrogen, and oxygen to moles. We know that the sample weighs 2.230 g and contains 76.59% carbon and 6.39% hydrogen, which means the rest must be oxygen. The mass of carbon in the sample is given by: Carbon Mass = (Total Mass) x (% Carbon/100) The mass of hydrogen in the sample is given by: Hydrogen Mass = (Total Mass) x (% Hydrogen/100) The mass of oxygen in the sample is given by: Oxygen Mass = Total Mass - Carbon Mass - Hydrogen Mass Now, we can convert these masses to moles by dividing by their molar masses.

Step 2: (a) Determine the empirical formula

To find the empirical formula, we need to find the molar ratio of carbon, hydrogen, and oxygen. Divide each element's moles by the smallest number of moles among them and then round to the nearest whole number: Empirical Formula ratio = (Carbon Moles / Min moles) : (Hydrogen Moles / Min moles) : (Oxygen Moles / Min moles)

Step 3: (b) Calculate moles of empirical formula

To find the molecular formula, first, find the molar mass of the empirical formula. Next, divide the given molar mass (94 g/mol) by the empirical formula's molar mass. This will give the integer factor by which the empirical formula must be multiplied to find the molecular formula. Molar Mass Ratio = Given Molar Mass / Empirical Formula Molar Mass

Step 4: (b) Determine the molecular formula

Finally, multiply each subscript in the empirical formula by the molar mass ratio determined above and then round to the nearest whole number. This will give the molecular formula for the compound.

Key Concepts

Molecular Formula Determination

To determine the molecular formula of a compound, one must first know its empirical formula and the molar mass. The empirical formula represents the simplest whole-number ratio of atoms in the compound.

Once the empirical formula is known, calculate its molar mass by adding the molar masses of all the atoms in the formula.

• The empirical formula molar mass serves as a basis to determine how many times its simple unit appears in the actual compound.

The molecular formula is then found by dividing the compound's given molar mass by the empirical formula's molar mass. This number, usually an integer, indicates how many times you need to multiply the empirical formula's subscripts to get the molecular formula.

For example:

• If the empirical formula is CH and its molar mass is 13 g/mol, and the compound's molar mass is 26 g/mol, then the molecular formula is C2H2, because 26 / 13 = 2.

Combustion Analysis

Combustion analysis is a common laboratory method used to determine the empirical formula of a compound, especially organic compounds. During combustion, the compound is burned in excess oxygen to produce carbon dioxide and water.

• From the amounts of CO2 and H2O produced, you can determine the amount of carbon and hydrogen in the original compound.

To perform combustion analysis, first, calculate the masses of carbon and hydrogen in CO2 and H2O. Then, convert these masses to moles using their respective atomic masses:

• Carbon: Using the mass of CO2 produced, subtract the mass of oxygen to find the carbon mass.
• Hydrogen: Similarly, convert the mass of H2O to find the hydrogen mass.
• Subtract these from the compound’s total mass to find any other element (like oxygen) in the compound.

This data can then be used to determine the empirical formula by comparing the mole ratios of the constituent elements.

Moles Calculation

Moles calculation is a fundamental concept in chemistry that is necessary to convert mass of elements to moles and vice versa. A mole is a standard unit in chemistry that represents Avogadro's number ( \( 6.022 \times 10^{23} \) particles). This conversion is pivotal in determining the composition and the empirical formula of compounds.

To calculate moles from mass, use the formula:

• Moles = Mass / Molar Mass

This formula allows us to convert the mass of an element or compound into moles, providing an easy way to compare amounts based on number of entities rather than mass.

For example:

• If you have 12 g of carbon ( \( \text{C} \)), dividing by its molar mass of 12 g/mol gives 1 mole of carbon.
• The conversion for hydrogen and oxygen follows similarly based on their molar weights of 1 g/mol and 16 g/mol respectively.

By converting masses to moles, it becomes feasible to calculate formulas which requires mole ratios, enabling the analysis of chemical compositions in reactions and compounds.