Problem 77 - Chemistry The Molecular Nature of Matter

Question

Phencyclidine ("angel dust") is \(\mathrm{C}_{17} \mathrm{H}_{25} \mathrm{~N}\). A sample suspected of being this illicit drug was found to have a percentage composition of \(84.71 \% \mathrm{C}, 10.42 \% \mathrm{H},\) and \(5.61 \% \mathrm{~N}\). Do these data acceptably match the theoretical data for phencyclidine?

Step-by-Step Solution

Answer

After computing the theoretical percent composition of C, H, and N in phencyclidine and comparing it to the given sample data, if the values closely align, the data acceptably matches.

Step 1: Calculate the percent composition of each element in phencyclidine

Use the molar mass of each element and the molecular formula to calculate the theoretical percent composition of carbon (C), hydrogen (H), and nitrogen (N) in phencyclidine. The molar masses are approximately 12.01 g/mol for carbon, 1.01 g/mol for hydrogen, and 14.01 g/mol for nitrogen. Multiply the number of each type of atom by its molar mass, then divide by the molecular weight of phencyclidine to get the percentage of each element.

Step 2: Find the molecular weight of phencyclidine

The molecular weight (MW) of phencyclidine can be calculated as follows: MW = (number of carbon atoms * molar mass of carbon) + (number of hydrogen atoms * molar mass of hydrogen) + (number of nitrogen atoms * molar mass of nitrogen). Then, sum the individual masses to find the total molecular weight.

Step 3: Calculate theoretical percent composition

Calculate the percentage by element as follows: Percent of C = (total mass of C / MW) * 100, Percent of H = (total mass of H / MW) * 100, Percent of N = (total mass of N / MW) * 100. On completing the calculations you would get - Percent of C = (17 * 12.01 / MW) * 100, Percent of H = (25 * 1.01 / MW) * 100, Percent of N = (1 * 14.01 / MW) * 100.

Step 4: Compare theoretical and experimental percent composition

After calculating the theoretical percent compositions, compare the values with the experimentally determined percentage composition data (84.71% C, 10.42% H, and 5.61% N) to determine if they reasonably match.

Step 5: Decide if the data is an acceptable match

If the theoretical percent composition values calculated in step 3 are close to the experimental values, it means the data matches and could confirm the presence of phencyclidine. Small discrepancies can be expected due to experimental errors.

Key Concepts

Theoretical Percent Composition

Understanding the theoretical percent composition of a compound is crucial when identifying substances and validating the purity of a sample. It involves the calculation of what percentage of the compound's total mass is made up of each constituent element.

For example, in the case of phencyclidine (C₁₇H₂₅N), we calculate this composition by first finding the molar mass of each element—approximately 12.01 g/mol for carbon, 1.01 g/mol for hydrogen, and 14.01 g/mol for nitrogen. We then multiply the number of atoms of each element in the molecular formula by its respective molar mass. The sum of these products gives us the total molecular weight of the compound.

By dividing the total mass of each element by the total molecular weight and then multiplying by 100, we obtain the theoretical percent composition for each element. These values provide a benchmark for comparing with experimental data to confirm the identity of a substance.

Molecular Weight Calculation

The molecular weight (MW) of a compound is the sum of the weights of all atoms present in the molecule. Calculating the MW is a vital step in determining percent composition.

To find the MW of a molecule like phencyclidine (C₁₇H₂₅N), we would perform the following steps: Multiply the number of carbon atoms (17) by the molar mass of carbon (12.01 g/mol), the number of hydrogen atoms (25) by the molar mass of hydrogen (1.01 g/mol), and the number of nitrogen atoms (1) by the molar mass of nitrogen (14.01 g/mol).

The sum of these calculations gives us the molecular weight of phencyclidine. Molecular weight is expressed in grams per mole (g/mol), representing the mass of one mole of a substance.

Empirical Formula Determination

Determining the empirical formula of a compound involves finding the simplest whole-number ratio of atoms present in a sample. The empirical formula may not always be the same as the molecular formula, but it gives the lowest whole-number ratio of the elements.

To ascertain the empirical formula, the percent composition must first be converted into moles by dividing by the atomic weight of each element. Once the moles are determined, these values are then divided by the smallest number of moles to obtain the simplest whole-number ratio.

For phencyclidine, the molecular formula is C₁₇H₂₅N. In some cases, this may also serve as the empirical formula. However, if the percentages resulted in different values, the true empirical formula might be a reduced form of the molecular formula. It is often an essential step for chemists when they analyze unknown compounds or confirm the identity of a synthesized substance.