Problem 90 - Chemistry and Chemical Reactivity

Question

In \(2006,\) a Russian team discovered an interesting molecule they called "sulflower" because of its shape and because it was based on sulfur. It is composed of \(57.17 \%\) S and \(42.83 \%\) C and has a molar mass of \(448.70 \mathrm{g} / \mathrm{mol} .\) Determine the empirical and molecular formulas of "sulflower."

Step-by-Step Solution

Answer

Empirical formula is SC₂; molecular formula is S₈C₁₆.

Step 1: Convert percentages to grams

Assume you have 100 grams of the compound. Therefore, you have 57.17 grams of sulfur (S) and 42.83 grams of carbon (C).

Step 2: Convert grams to moles

Use the molar mass of sulfur (32.07 g/mol) and carbon (12.01 g/mol) to convert grams to moles:For sulfur: \( \frac{57.17 \text{ g}}{32.07 \text{ g/mol}} = 1.782 \text{ mol S} \)For carbon: \( \frac{42.83 \text{ g}}{12.01 \text{ g/mol}} = 3.566 \text{ mol C} \)

Step 3: Determine the simplest mole ratio

Divide each mole amount by the smallest number of moles calculated to find the simplest integer ratio:\[\frac{1.782 \text{ mol S}}{1.782} = 1 \text{ S}\]\[\frac{3.566 \text{ mol C}}{1.782} \approx 2 \text{ C}\]This gives an empirical formula of SC extsubscript{2}.

Step 4: Calculate the molar mass of the empirical formula

The empirical formula SC extsubscript{2} has a molar mass of:\(32.07 \text{ g/mol} + 2(12.01 \text{ g/mol}) = 56.09 \text{ g/mol}\)

Step 5: Determine the molecular formula

To find the molecular formula, divide the molar mass of the compound by the molar mass of the empirical formula:\[\frac{448.70 \text{ g/mol}}{56.09 \text{ g/mol}} \approx 8\]Multiply the subscripts in the empirical formula by 8 to get the molecular formula: S extsubscript{8}C extsubscript{16}.

Key Concepts

Percentage Composition

Understanding percentage composition is crucial when analyzing compounds like "sulflower." Percentage composition tells us the relative mass of each element in a compound compared to its total mass. In this exercise, the compound is made up of 57.17% sulfur (S) and 42.83% carbon (C). By assuming a 100 g sample of the compound, the percentages directly translate to masses:

• Sulfur: 57.17 g
• Carbon: 42.83 g

This approach simplifies calculations because it aligns the percentages with measurable amounts. It sets the stage for further finding out quantities in moles, a foundational step in determining empirical and molecular formulas of a substance.

Mole Ratio

The mole ratio is key to finding the empirical formula. Start by converting the mass of each element to moles, using their respective molar masses:

• Sulfur's molar mass is 32.07 g/mol, resulting in 1.782 mol S for 57.17 g.
• Carbon's molar mass is 12.01 g/mol, resulting in 3.566 mol C for 42.83 g.

Next, identify the simplest whole-number ratio by dividing each mole quantity by the smallest number of moles calculated:- S: \( \frac{1.782}{1.782} = 1 \)- C: \( \frac{3.566}{1.782} \approx 2 \)This gives a simple ratio of 1 mole of sulfur to 2 moles of carbon, leading to the empirical formula SC₂. This mole ratio reflects the basic unit proportions of elements in "sulflower."

Molar Mass Calculation

Once you have determined the empirical formula, the next step involves calculating its molar mass. For SC₂, compute as follows: - Sulfur: 32.07 g/mol - Carbon (two atoms): 2 x 12.01 g/mol = 24.02 g/mol - Total molar mass of SC₂: 32.07 + 24.02 = 56.09 g/mol The empirical formula's molar mass helps to compare with the known molar mass of the compound to deduce its molecular formula. Here, the empirical formula is much lighter than the known molar mass of the compound, hinting that multiple empirical formula units combine to form one molecule of "sulflower."

Empirical Formula Determination

Determining the empirical formula involves the steps below: 1. Convert the percentage of each element to mass in grams assuming 100 g of the compound. 2. Calculate the moles of each element using their molar masses. 3. Divide each element's mole value by the smallest mole value to determine the simplest mole ratio. For "sulflower," this ratio of S to C was found to be 1:2, resulting in the empirical formula SC₂.

Molecular Formula

The molecular formula is determined by comparing the molar mass of the empirical formula to the compound's full molar mass, which is given as 448.70 g/mol. Divide this by the empirical formula molar mass (56.09 g/mol), which yields approximately 8. Multiply each subscript in the empirical formula SC₂ by 8 to find the molecular formula: S₈C₁₆. This indicates the true number of atoms in each molecule of "sulflower."