Question

A compound isolated from the rind of lemons is found to be \(88.14 \%\) carbon and \(11.86 \%\) hydrogen by mass. How many grams of \(\mathrm{C}\) and \(\mathrm{H}\) are there in a \(100.0-\mathrm{g}\) sample of this substance? How many moles of \(\mathrm{C}\) and \(\mathrm{H}\) ? What is the empirical formula? The molar mass is determined to be \(136.26 \mathrm{~g} / \mathrm{mol} .\) What is the molecular formula? Which step of the process just described does your group understand the least? Which step will be hardest for the members of your group to remember?

Short answer

There are 88.14 g of C and 11.86 g of H in a 100.0 g sample. This corresponds to 7.337 moles of C and 11.77 moles of H. The empirical formula is CH and the molecular formula is C6H6. The hardest step to remember might be the conversion of mass percentages to moles and using these to discern the molecular formula.

Step-by-step solution

Calculate the mass of carbon and hydrogen

To find the mass of carbon and hydrogen in the sample, multiply the percentage by the total mass of the sample. For carbon, it's 88.14% of 100.0 g and for hydrogen, it's 11.86% of 100.0 g.

Convert the masses to moles

Use the molar mass of carbon (12.01 g/mol) and hydrogen (1.008 g/mol) to convert the mass of each element to moles by dividing the mass of each element by its molar mass.

Find the simplest whole number ratio

Divide the moles of each element by the smallest number of moles calculated in step 2 to find the simplest whole number ratio.

Write the empirical formula

Use the whole number ratio to write the empirical formula by assigning each ratio as a subscript to the respective element.

Calculate the empirical formula mass

Add up the masses of the atoms in the empirical formula to find the empirical formula mass.

Determine the molecular formula

Divide the given molar mass of the compound by the empirical formula mass to find the multiplier. Multiply the subscripts in the empirical formula by this multiplier to find the molecular formula.

Understanding the process

It is crucial to closely follow each step, as understanding how to convert mass percent to mass, mass to moles, and use the mole ratio to find empirical and molecular formulas, is key to solving the problem. Recalling the molar masses and keeping track of mole conversions can be challenging.

Key concepts

Mole Concept

The mole concept is a central idea in chemistry that enables us to count atoms, molecules, and ions by weighing. One mole is defined as the amount of substance containing the same number of entities (atoms, molecules, ions, etc.) as there are atoms in 12 grams of carbon-12. This number is Avogadro's number, which is approximately 6.022 \( \times \) 10^23 entities. In practice, to calculate the number of moles of an element or compound, you need to know the mass of the sample and its molar mass. Then, you divide the mass by the molar mass to obtain the moles.

Using the mole concept allows chemists to work with the macroscopic quantities of materials they handle in the lab while being able to calculate the number of atoms or molecules they contain. This is crucial in stoichiometry, which involves the measurement of these quantities during chemical reactions.

Mass Percent Composition

Mass percent composition is a measurement of the concentration of each element within a compound. It reflects the mass of a specific element in a compound as a percentage of the total mass of that compound. To calculate the mass percent of an element, you take the mass of the element in the sample and divide it by the total mass of the sample, then multiply the result by 100% to get the percent composition.

For instance, if a sample is said to contain 88.14% carbon, it means that in every 100 grams of the compound, there are 88.14 grams of carbon. Knowing the mass percent composition is essential in determining the empirical formula of a substance, which is the simplest whole number ratio of atoms in a compound.

Molar Mass

Molar mass is defined as the mass of one mole of a substance. It is usually expressed in units of grams per mole (g/mol). The molar mass of an element is the atomic weight listed on the periodic table in g/mol. For a compound, the molar mass is the sum of the atomic weights of all the atoms in the molecular formula.

For example, the molar mass of carbon is 12.01 g/mol, which means one mole of carbon atoms weighs 12.01 grams. In a given chemical reaction or composition calculation, knowing the molar mass is essential to convert between mass and moles, allowing for proper stoichiometric calculations.

Stoichiometry

Stoichiometry is the section of chemistry that involves the quantitative relationships between reactants and products in a chemical reaction. It's based on the law of conservation of mass and the concept that matter is neither created nor destroyed in chemical reactions. Practically, stoichiometry is used to predict the amounts of products that will form in a given reaction based on the amounts of reactants used.

It calculates the reactants needed or products formed using the mole ratio obtained from the balanced chemical equation. The mole concept, mass percent composition, and molar mass are all critical components when performing stoichiometric calculations. They enable us to convert between mass, moles, and numbers of particles, making stoichiometry a core part of understanding chemical reactions.