Problem 89 - Chemistry The Molecular Nature of Matter

Question

When \(0.684 \mathrm{~g}\) of an organic compound containing only carbon, hydrogen, and oxygen was burned in oxygen, \(1.312 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(0.805 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) were obtained. What is the empirical formula of the compound?

Step-by-Step Solution

Answer

The empirical formula is obtained by dividing the number of moles of carbon, hydrogen, and oxygen by the smallest number of moles of these elements.

Step 1: Calculate moles of carbon in CO2

Using the molar mass of CO2 (44.01 g/mol), convert the mass of CO2 to moles to find the moles of carbon: carbon moles = mass of CO2 / molar mass of CO2 = 1.312 g / 44.01 g/mol

Step 2: Calculate moles of hydrogen in H2O

Using the molar mass of H2O (18.02 g/mol), convert the mass of H2O to moles to find the moles of hydrogen (since each mole of water contains 2 moles of hydrogen atoms): hydrogen moles = (mass of H2O / molar mass of H2O) * 2 = (0.805 g / 18.02 g/mol) * 2

Step 3: Calculate moles of oxygen in the organic compound

Subtract the mass of carbon and hydrogen (as part of CO2 and H2O) from the total mass of the organic compound to get the mass of oxygen. Then divide by oxygen's molar mass (16.00 g/mol) to get moles of oxygen:mass of oxygen = total mass of compound - (mass of carbon + mass of hydrogen)oxygen moles = mass of oxygen / molar mass of oxygen

Step 4: Determine empirical formula

Divide the moles of carbon, hydrogen, and oxygen by the smallest number of moles to determine the simplest whole number ratio. The resulting numbers are the subscripts of the elements in the empirical formula.

Key Concepts

Stoichiometry

Stoichiometry is akin to a recipe in chemistry. Just like in cooking, you need the right amount of each ingredient, stoichiometry tells you the exact amount of reactants you need to react together to form products in a chemical reaction. It's based on the conservation of mass where all atoms that enter a reaction must be accounted for in the products.

In the exercise, stoichiometry is used to relate the mass of an organic compound that was burned to the amounts of carbon dioxide and water produced in the reaction. We used the stoichiometric coefficients from the balanced chemical equation for the combustion of an organic compound to understand the amount of each element in the product. The process involves determining the ratios in which the elements combine, which are then used to determine the empirical formula of the original compound.

Molar Mass

The molar mass of a substance is the weight of 6.022 x 10²³ (Avogadro's number) of its particles (atoms, molecules, ions, etc.), typically expressed in grams per mole (g/mol). Finding the molar mass is essential for converting between mass and moles of a substance.

In our example, we used the molar masses of carbon dioxide (CO₂) and water (H₂O) to convert the mass of these compounds to moles. Knowing the molar mass of CO₂ is 44.01 g/mol and that of H₂O is 18.02 g/mol, we used these values to find out how many moles of carbon and hydrogen are present after combustion.

Combustion Analysis

Combustion analysis is a method in chemistry for determining the elemental composition of a pure compound by burning it in excess oxygen and analyzing the amounts of products formed. It's particularly useful for organic compounds that are composed of carbon, hydrogen, and oxygen.

The analysis involves measuring the masses of carbon dioxide and water produced, which will later help in quantifying the actual amounts of carbon and hydrogen in the initial compound. Oxygen is then determined by the difference in mass from the original compound. The data from combustion analysis feeds directly into stoichiometric calculations to help determine the empirical formula of the compound.

Moles Calculation

The mole is a fundamental unit in chemistry used to measure quantity. One mole of any substance contains the same number of entities (like atoms or molecules) as there are atoms in exactly 12 grams of carbon-12, which is approximately 6.022 x 10²³ entities.

In the given exercise, calculating moles was the next step after finding the masses of CO₂ and H₂O. The mass of each compound was divided by its molar mass to find the number of moles of CO₂ and H₂O, which then allowed for the determination of the moles of carbon and hydrogen. For oxygen, we subtracted the masses of carbon and hydrogen from the total mass of the organic compound to find the mass of oxygen, which we then converted to moles.