Problem 98 - Chemistry The Molecular Science

Question

A well-known reagent in analytical chemistry, dimethylglyoxime, has the empirical formula \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{NO} .\) If its molar mass is \(116.1 \mathrm{~g} / \mathrm{mol}\), determine the molecular formula of the compound.

Step-by-Step Solution

Answer

The molecular formula of dimethylglyoxime is \(\mathrm{C}_4\mathrm{H}_8\mathrm{N}_2\mathrm{O}_2\).

Step 1: Calculate Empirical Formula Mass

First, we need to find the molar mass of the empirical formula \(\mathrm{C}_2\mathrm{H}_4\mathrm{NO}\). Let's calculate it using the atomic masses: \(C: 12.01 \, \text{g/mol}, \ H: 1.008 \, \text{g/mol}, \ N: 14.01 \, \text{g/mol}, \ O: 16.00 \, \text{g/mol}.\)The empirical formula mass is then:\[2(12.01) + 4(1.008) + 14.01 + 16.00 = 58.08 \, \text{g/mol}.\]

Step 2: Determine Multiplication Factor

Next, determine how many times the empirical formula mass fits into the given molar mass of the compound. Divide the molar mass by the empirical formula mass:\[\frac{116.1}{58.08} \approx 2.\]This indicates that the molecular formula is twice the empirical formula.

Step 3: Calculate Molecular Formula

Multiply each element in the empirical formula \(\mathrm{C}_2\mathrm{H}_4\mathrm{NO}\) by the factor determined in Step 2 (which is 2):- Carbon: \(2 \times 2 = 4\)- Hydrogen: \(4 \times 2 = 8\)- Nitrogen: \(1 \times 2 = 2\)- Oxygen: \(1 \times 2 = 2\)Thus, the molecular formula is \(\mathrm{C}_4\mathrm{H}_8\mathrm{N}_2\mathrm{O}_2\).

Key Concepts

Empirical Formula Calculation

Empirical formula calculation is all about finding the simplest whole number ratio of atoms in a compound. This is the starting point for determining a molecular formula. To calculate an empirical formula, you need the number of moles of each element in a given sample. For example, if your compound is composed of certain percentages of elements, you first convert these percentages to grams. However, if you already have the elemental composition in grams, you can move straight to finding moles.

• Convert the mass of each element to moles by dividing by its atomic mass.
• Divide all the mole values obtained by the smallest mole value among them. This will give you a mole ratio.
• Use these ratios as subscripts in your empirical formula. If necessary, multiply these ratios by a whole number to get them all to close to whole number values.

After these steps, you have the empirical formula, which reveals the simplest ratio of all elements present in the compound. The empirical formula is critical because it reflects the core composition, which is fundamental in analytical chemistry for understanding molecular structures.

Empirical Formula Mass

Empirical formula mass is the sum of the atomic masses of all the elements in the empirical formula. This value helps in determining how the empirical formula relates to the actual molecular formula. In our example, for dimethylglyoxime, the empirical formula is \(\mathrm{C}_2\mathrm{H}_4\mathrm{NO}\). To find its empirical formula mass, you calculate:

• Carbon: \(2 \times 12.01\, \text{g/mol} = 24.02\, \text{g/mol}\)
• Hydrogen: \(4 \times 1.008\, \text{g/mol} = 4.032\, \text{g/mol}\)
• Nitrogen: \(1 \times 14.01\, \text{g/mol} = 14.01\, \text{g/mol}\)
• Oxygen: \(1 \times 16.00\, \text{g/mol} = 16.00\, \text{g/mol}\)

Adding these values gives the empirical formula mass: \(58.08\, \text{g/mol}\). This number is essential because it establishes a baseline for comparing with the molecular mass. By dividing the compound's molar mass by the empirical formula mass, we determine the multiplication factor to find the molecular formula.

Analytical Chemistry

Analytical chemistry focuses on analyzing substances to determine their chemical compositions. It encompasses a variety of techniques, including calculating empirical and molecular formulas based on experimental data like percentage composition or measured masses.
In the context of the problem, analytical chemistry uses:

• The empirical formula mass as a tool to connect a compound's basic ratio of elements to its actual molecular structure.
• Comparative analysis by dividing molecular mass by empirical formula mass to provide insights into the compound's molecular formula.

Analytical chemistry is fundamental in identifying unknown substances, ensuring product purity, and conducting research on new chemical compounds. Understanding these principles makes it easier to derive meaningful insights from chemical formulas and properties, directly guiding practical applications and furthering scientific discovery.