Question

Tetraphenylporphyrin is a synthetic compound that resembles naturally occurring porphyrins. Porphyrins are found in hemoglobin and cytochromes, which are important to biological functions in humans. Tetraphenylporphyrin is composed of only \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{N}\) atoms. Experiments show that tetraphenylporphyrin is \(85.96 \% \mathrm{C}\) and \(4.92 \% \mathrm{H}\) by mass. What is the empirical formula of tetraphenylporphyrin?

Short answer

The empirical formula of tetraphenylporphyrin is C11H7N.

Step-by-step solution

Determine the mass percentages of all elements

First, we have the mass percentage of carbon (C) and hydrogen (H) given in the problem. To find the mass percentage of nitrogen (N), subtract the sum of carbon and hydrogen percentages from 100%: Percentage of nitrogen = 100% - (85.96% + 4.92%) Percentage of nitrogen = 9.12% Now we have mass percentages of all elements: - Carbon (C): 85.96% - Hydrogen (H): 4.92% - Nitrogen (N): 9.12%

Convert mass percentages to grams

Let's assume we have a 100 g sample of the compound, then the mass of each element in the sample will be equal to its mass percentage: - Mass of carbon (C): 85.96 g - Mass of hydrogen (H): 4.92 g - Mass of nitrogen (N): 9.12 g

Convert grams to moles

Now, we will convert the mass of each element to moles using their respective molar masses: - Moles of carbon (C): \(\frac{85.96 g}{12.01 g mol^{-1}} = 7.16 mol\) - Moles of hydrogen (H): \(\frac{4.92 g}{1.01 g mol^{-1}} = 4.87 mol\) - Moles of nitrogen (N): \(\frac{9.12 g}{14.01 g mol^{-1}} = 0.651 mol\)

Find the mole ratio

Now, we will find the ratio of moles of each element by dividing all the moles by the smallest number of moles: - Carbon:nitrogen:hydrogen ratio = \(\frac{7.16}{0.651} : 1 : \frac{4.87}{0.651}\) - Carbon:nitrogen:hydrogen ratio = 11 : 1 : 7.5 The ratio is close to whole numbers. To convert the ratio to whole numbers, it can be rounded: - Carbon:nitrogen:hydrogen ratio ≈ 11:1:7

Determine the empirical formula

Based on the whole number ratio obtained in the previous step, the empirical formula of tetraphenylporphyrin is: C11H7N1 or C11H7N

Key concepts

Chemical Composition Analysis

Chemical composition analysis is a fundamental process in chemistry that helps in understanding the proportion of different elements in a compound. By breaking down a compound's percentage composition by mass, we can identify the amount of each element present. In the example of tetraphenylporphyrin, it is composed of carbon, hydrogen, and nitrogen. The problem provides the mass percentages of carbon and hydrogen, with the remainder being nitrogen.

• Carbon makes up 85.96% of the compound.
• Hydrogen consists of 4.92%.
• Nitrogen fills the remaining 9.12% of the composition.

By understanding these percentages, the analysis allows us to eventually calculate the empirical formula. This percentage-based breakdown serves as the basis for further conversion processes like determining moles and simplifying ratios, which are crucial for deeper insights into the compound's composition.

Molecular Formula Determination

The process of determining a molecular formula involves several steps that convert mass percentages into a more descriptive formula that shows the ratio of atoms in the compound. The empirical formula offers the simplest whole-number ratio, but the molecular formula provides the actual number of each type of atom in the molecule.
First, convert the mass percentages into grams assuming a 100 g sample, which gives us a straightforward conversion where the mass percentage equals the mass in grams.
Next, convert this mass into moles by dividing each element's mass by its molar mass:

• Carbon: 85.96 g ÷ 12.01 g/mol = 7.16 moles
• Hydrogen: 4.92 g ÷ 1.01 g/mol = 4.87 moles
• Nitrogen: 9.12 g ÷ 14.01 g/mol = 0.651 moles

Then, to find the simplest ratio of these elements, divide each mole value by the smallest number of moles. This yields the mole ratio, which is then rounded to the nearest whole number to give the empirical formula. For tetraphenylporphyrin, this ratio results in the formula C\(_{11}\)H\(_7\)N. If additional molecular data is known, such as molar mass, it can allow conversion of this empirical formula to the molecular formula, providing a more detailed representation of the compound.

Porphyrins

Porphyrins are fascinating organic compounds with a critical role in many biological systems. They possess a distinct structural motif consisting of four pyrrole rings connected through methine bridges, forming a macrocycle called a porphyrin ring.
Porphyrins are crucial because they form the core structure of heme, which is essential for oxygen transport in hemoglobin and other vital biochemical processes. In cytochromes, porphyrins play a role in electron transport and energy transfer. Synthetic porphyrins, like tetraphenylporphyrin, mimic the naturally occurring ones but can be altered to perform specific functions or serve as models in scientific research. Understanding the basic makeup of porphyrins, including the empirical formula, allows scientists to manipulate these molecules for applications ranging from medical therapies to advanced materials.
Thus, porphyrins are not only structurally important but also have significant functional implications in both nature and synthetic applications.