Problem 76 - Chemistry An Atoms First Approach

Question

Arrange the following substances in order of increasing mass percent of carbon. a. caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{O}_{2}\) b. sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) c. ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)

Step-by-Step Solution

Answer

The substances arranged in order of increasing mass percent of carbon are: 1. Sucrose (\(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\)): 42.11% carbon 2. Caffeine (\(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{O}_{2}\)): 49.48% carbon 3. Ethanol (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)): 52.17% carbon

Step 1: Calculate the molar mass of each substance

For this, we'll need the molar mass of each element (C, H, N, and O), which are approximately 12 g/mol, 1 g/mol, 14 g/mol, and 16 g/mol, respectively. a. Caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{O}_{2}\) Molar mass = (8 × 12) + (10 × 1) + (4 × 14) + (2 × 16) = 194 g/mol b. Sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) Molar mass = (12 × 12) + (22 × 1) + (11 × 16) = 342 g/mol c. Ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) Molar mass = (2 × 12) + (6 × 1) + (1 × 16) = 46 g/mol

Step 2: Calculate the mass of carbon in each substance

Next, we will find the mass of carbon in each substance. a. Caffeine: 8 atoms of carbon, each with a mass of 12 g/mol, so the mass of carbon = 8 × 12 = 96 g/mol b. Sucrose: 12 atoms of carbon, each with a mass of 12 g/mol, so the mass of carbon = 12 × 12 = 144 g/mol c. Ethanol: 2 atoms of carbon, each with a mass of 12 g/mol, so the mass of carbon = 2 × 12 = 24 g/mol

Step 3: Calculate the mass percent of carbon in each substance

Now, we can find the mass percent of carbon in each substance: a. Caffeine: (mass of carbon / molar mass) × 100 = (96 / 194) × 100 = 49.48% b. Sucrose: (mass of carbon / molar mass) × 100 = (144 / 342) × 100 = 42.11% c. Ethanol: (mass of carbon / molar mass) × 100 = (24 / 46) × 100 = 52.17%

Step 4: Arrange the substances in increasing order of mass percent of carbon

Now that we have the mass percent of carbon for each substance, we can arrange them in increasing order: 1. Sucrose: 42.11% carbon 2. Caffeine: 49.48% carbon 3. Ethanol: 52.17% carbon

Key Concepts

Molar Mass Calculation

Understanding how to calculate the molar mass is essential in chemistry, especially when dealing with chemical substances. The molar mass is essentially the weight of one mole of a substance. To compute this, we need to know the molar masses of the elements involved:

• Carbon (C): approximately 12 g/mol
• Hydrogen (H): approximately 1 g/mol
• Nitrogen (N): approximately 14 g/mol
• Oxygen (O): approximately 16 g/mol

Once you have these values, you can calculate the molar mass by multiplying the number of each type of atom by its respective molar mass, and then summing all these values. Let's look at a common example, caffeine: The molar mass of caffeine \( \mathrm{C}_{8} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{O}_{2} \) can be calculated as follows:\[(8 \times 12) + (10 \times 1) + (4 \times 14) + (2 \times 16) = 194 \text{ g/mol}\] This calculation lays the foundation for understanding the composition of any chemical substance.

Chemical Composition

The chemical composition of a substance tells us the elements it is made up of and in what proportions. This is crucial for understanding how the substance behaves in different chemical reactions or environments. In the exercise, we examined substances with chemical formulas:

• Caffeine: \( \mathrm{C}_{8}\mathrm{H}_{10}\mathrm{N}_{4}\mathrm{O}_{2} \)
• Sucrose: \( \mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11} \)
• Ethanol: \( \mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH} \)

Each chemical formula shows the different atoms involved and how many of each are present. For example, caffeine has 8 carbon atoms, 10 hydrogen atoms, 4 nitrogen atoms, and 2 oxygen atoms. This information is key when performing any calculations relating to chemical or physical properties, such as determining the mass percent of an element, like carbon, in the substance.

Knowing the chemical composition helps chemists predict how substances can react or bind with each other.

Chemical Formula Analysis

Chemical formula analysis involves examining the given chemical formula to extract meaningful information about the substance it represents.Analyzing a chemical formula starts with identifying the number of atoms of each element present. This requires an understanding of subscript numbers in chemical formulas. For instance, in \( \mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11} \), there are 12 carbon atoms, 22 hydrogen atoms, and 11 oxygen atoms. Breaking down a formula allows us to determine other properties, such as the mass percent of an element like carbon. Here’s how we derive the mass percent:

• Calculate the total mass of all carbon atoms:
  \( 12 \times 12 \text{ g/mol} = 144 \text{ g/mol} \) for carbon in sucrose.
• Divide by the total molar mass, then multiply by 100:
  \( \frac{144}{342} \times 100 = 42.11\% \)

Chemical formula analysis provides a deep dive into the quantitative aspects of a substance, unveiling ratios and percentages crucial for understanding its behavior and reactivity.