Question

Which of the following sets of information allows you to obtain the molecular formula of a covalent compound? In each case that allows it, explain how you would proceed (draw a road map and write a plan for a solution). (a) Number of moles of each type of atom in a given sample of the compound (b) Mass \% of each element and the total number of atoms in a molecule of the compound (c) Mass \% of each element and the number of atoms of one element in a molecule of the compound (d) Empirical formula and mass \(\%\) of each element (e) Structural formula

Short answer

(a), (b), (c), (d), and (e) provide sufficient information to determine the molecular formula.

Step-by-step solution

Understand the Requirement

The problem asks to determine which sets of information allow obtaining the molecular formula of a covalent compound. Additionally, for each valid case, an explanation or roadmap with a step-by-step solution is required.

Analyze Option (a)

Given: Number of moles of each type of atom in a sample of the compound. Solution: This provides the exact ratio of atoms in the compound. Using these moles, one can determine the empirical formula and then, if the molecular mass is known, the molecular formula can be found. Therefore, this information is sufficient.

Analyze Option (b)

Given: Mass % of each element and the total number of atoms in a molecule. Solution: Convert mass % into grams, convert grams to moles, convert moles to a ratio, and then determine the empirical formula. The total number of atoms can help to scale the empirical formula to the molecular formula. Thus, this information is sufficient.

Analyze Option (c)

Given: Mass % of each element and the number of atoms of one element in a molecule. Solution: Use mass % to get the moles of each element. Comparing the moles ratio with the provided number of atoms of one element, scale to get the molecular formula. Hence, this information is sufficient.

Analyze Option (d)

Given: Empirical formula and mass % of each element. Solution: Knowing both empirical formula and mass % allows calculating the molecular mass and thus deducing the molecular formula. So, this information is sufficient.

Analyze Option (e)

Given: Structural formula. Solution: The structural formula directly indicates the number and arrangement of atoms in the molecule, so the molecular formula can be derived easily. This information is sufficient.

Key concepts

Empirical Formula

Calculating the empirical formula is crucial in understanding the composition of covalent compounds. The empirical formula shows the simplest whole-number ratio of atoms in a compound. For instance, if you have a sample with 40% carbon, 6.7% hydrogen, and 53.3% oxygen by mass, you first convert these percentages to grams (assuming 100 grams of total compound, it would be 40g of C, 6.7g of H, and 53.3g of O). Next, convert these masses to moles by dividing by their respective atomic masses (C: 12.01 g/mol, H: 1.01 g/mol, O: 16.00 g/mol). The mole values are then expressed in the simplest whole number ratio to get the empirical formula. If you find the empirical formula to be CH2O, it tells you the ratio of atoms, but not necessarily the exact count in each molecule, which would require further information, like the molecular mass.

Mass Percentage Composition

Understanding mass percentage composition helps in determining the relative amounts of each element in a compound. The mass percentage composition can be found by taking the mass of a particular element within the compound divided by the total mass of the compound, then multiplying by 100. For example, in a compound with a molecular formula of C6H12O6 (glucose), to find the mass percentage of carbon: calculate the total mass of six carbon atoms (6 x 12.01 g/mol) and divide it by the molar mass of the compound (180.16 g/mol), then multiply by 100%. This would give approximately 40% carbon. This percentage allows the determination of how much each element contributes to the total mass of the compound, which is important when calculating empirical formula and verifying molecular formulas.

Moles of Atoms

Moles of atoms give us a direct pathway to finding the empirical formula by showing how many atoms of each element are present in a substance. The mole ratio of atoms is found by converting the masses of the elements in the compound into moles. Suppose you know that a compound contains 0.1 moles of hydrogen and 0.05 moles of oxygen, you can deduce the simplest mole ratio by dividing both values by the smallest number (in this case, 0.05). This would give a ratio of 2:1, leading to the empirical formula H2O. If additional data, such as the molecular weight, is available, it can help to convert the empirical formula to the molecular formula providing the exact count of atoms in a molecule.

Structural Formula

The structural formula is a detailed representation that offers a clear view of the number and arrangement of atoms in a molecule. Unlike the molecular and empirical formulas, which only provide the types and ratios of atoms, the structural formula showcases how these atoms are connected. For example, the structural formula of ethanol (C2H5OH) not only tells you there are two carbon atoms, six hydrogen atoms, and one oxygen atom, but also how these atoms are bonded to each other: one hydroxyl group (-OH) attached to a carbon chain (C-C). Understanding the structural formula helps in visualizing the molecule in three dimensions, predicting molecule behavior, and understanding reactions and interactions. With the structural formula at hand, determining the molecular formula becomes simple: count the total atoms of each element to derive the exact molecular composition.