Question

Calculate the mass in grams of hydrogen present in \(2.500 \mathrm{~g}\) of each of the following compounds. a. benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\) b. calcium hydride, \(\mathrm{CaH}_{2}\) c. ethyl alcohol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) d. serine, \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{O}_{3} \mathrm{~N}\)

Short answer

The mass of hydrogen in grams present in 2.500 g of each compound is: - Benzene: \(1.1675 \mathrm{g}\) - Calcium hydride: \(0.1200 \mathrm{g}\) - Ethyl alcohol: \(0.3285 \mathrm{g}\) - Serine: \(0.16825 \mathrm{g}\)

Step-by-step solution

Calculate the molar mass of each compound

First, we need to find the molar mass for each compound: - Benzene (C6H6): 6 * 12.01 (C) + 6 * 1.01 (H) = 78.12 g/mol - Calcium hydride (CaH2): 40.08 (Ca) + 2 * 1.01 (H) = 42.10 g/mol - Ethyl alcohol (C2H5OH): 2 * 12.01 (C) + 6 * 1.01 (H) + 16.00 (O) = 46.08 g/mol - Serine (C3H7O3N): 3 * 12.01 (C) + 7 * 1.01 (H) + 3 * 16.00 (O) + 14.01 (N) = 105.12 g/mol

Calculate the mass percent of hydrogen in each compound

Next, we need to find the mass percent of hydrogen in each compound: - Benzene (C6H6): (6 * 1.01 g)/(78.12 g/mol) * 100% = 46.70 % - Calcium hydride (CaH2): (2 * 1.01 g)/(42.10 g/mol) * 100% = 4.80 % - Ethyl alcohol (C2H5OH): (6 * 1.01 g)/(46.08 g/mol) * 100% = 13.14 % - Serine (C3H7O3N): (7 * 1.01 g)/(105.12 g/mol) * 100% = 6.73 %

Calculate the mass of hydrogen in grams in each compound

We are given that we have 2.500 g of each compound. Now we can find the mass of hydrogen in each compound by using the mass percent of hydrogen in each compound: - Benzene (C6H6): 2.500 g * 46.70% = 1.1675 g - Calcium hydride (CaH2): 2.500 g * 4.80% = 0.1200 g - Ethyl alcohol (C2H5OH): 2.500 g * 13.14% = 0.3285 g - Serine (C3H7O3N): 2.500 g * 6.73% = 0.16825 g So, the mass of hydrogen in each compound is as follows: - Benzene: 1.1675 g - Calcium hydride: 0.1200 g - Ethyl alcohol: 0.3285 g - Serine: 0.16825 g

Key concepts

Molar Mass Calculation

Understanding how to calculate the molar mass is essential in chemistry, especially in stoichiometry problems. It's the mass of one mole of a substance, usually expressed in grams per mole (g/mol). The molar mass is calculated by summing the atomic masses of all the atoms in a molecule.

For example, benzene, with the formula \( \mathrm{C}_{6} \mathrm{H}_{6} \), consists of six carbon atoms and six hydrogen atoms. To calculate its molar mass, multiply the atomic mass of carbon (12.01 g/mol) by 6 and the atomic mass of hydrogen (1.01 g/mol) by 6, then add the results together. The same process applies to other compounds, such as calcium hydride, ethyl alcohol, and serine.

This step is crucial because it sets the foundation for finding out how much of a particular element is present in a sample of a compound. Always double-check your work for accuracy as a small error here can affect the subsequent calculations.

Mass Percent Composition

After calculating the molar mass, the mass percent composition tells us what fraction of the total mass of a compound is made up by a particular element. This is particularly useful for understanding the composition of compounds and is a key step in stoichiometry.

The mass percent composition is found by dividing the total mass of the element in the compound by the total molar mass of the compound, then multiplying by 100 to get a percentage. For example, in ethyl alcohol (\( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \)), the mass percent of hydrogen is calculated by taking the mass of hydrogen atoms (6 * 1.01g) divided by the molar mass of ethyl alcohol (46.08 g/mol), and then multiplying by 100%.

To improve comprehension, consider visualizing the compound as a pie chart with each element's mass percent as a slice of the pie. This visual can help students better grasp the concept of mass percent composition.

Chemical Compound Analysis

Once you know the molar mass and mass percent composition, you can dive into chemical compound analysis. This process involves using these values to determine the amount of each element present in a sample of a compound.

For instance, the textbook exercise queries the mass of hydrogen in a 2.500 g sample of different compounds. Using the mass percent composition, you can calculate the exact grams of hydrogen present. Simply multiply the sample's mass by the mass percent of hydrogen for each compound. For serine (\( \mathrm{C}_{3} \mathrm{H}_{7} \mathrm{O}_{3} \mathrm{N} \)), this equates to 2.500 g * 6.73%, yielding 0.16825 g of hydrogen.

Remember that in real-world applications, this kind of analysis has vast implications, from determining nutritional content in food to quality control in the pharmaceutical industry. When solving problems, focus on the logic behind each step to not only arrive at an accurate answer but also to understand why each step is necessary.