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, \(\bar{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) c. ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)

Short answer

The order of increasing mass percent of carbon for the given substances is: Sucrose (42.11%), Caffeine (49.48%), and Ethanol (52.14%).

Step-by-step solution

Write down the formula of each compound

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: \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)

Calculate the molar mass of each compound

We will now calculate the molar mass of each compound by multiplying the number of each element in the compound by its molar mass, then summing the products. Using the periodic table, we can find the molar mass of each element: Carbon: 12.01 g/mol Hydrogen: 1.01 g/mol Nitrogen: 14.01 g/mol Oxygen: 16.00 g/mol a. Caffeine: Molar mass = (8 × 12.01) + (10 × 1.01) + (4 × 14.01) + (2 × 16.00) = 194.19 g/mol b. Sucrose: Molar mass = (12 × 12.01) + (22 × 1.01) + (11 × 16.00) = 342.30 g/mol c. Ethanol: Molar mass = (2 × 12.01) + (6 × 1.01) + (1 × 16.00) = 46.07 g/mol

Calculate the mass percent of carbon for each compound

We will now determine the mass percent of carbon for each compound by dividing the total mass of carbon atoms in each compound by the compound's molar mass, then multiplying by 100% to get the mass percent. a. Caffeine: Mass percent of carbon = (8 × 12.01 / 194.19) × 100% ≈ 49.48% b. Sucrose: Mass percent of carbon = (12 × 12.01 / 342.30) × 100% ≈ 42.11% c. Ethanol: Mass percent of carbon = (2 × 12.01 / 46.07) × 100% ≈ 52.14%

Arrange the substances in order of increasing mass percent of carbon

Now that we have calculated the mass percent of carbon for each substance, we can arrange them accordingly: 1. Sucrose (42.11%) 2. Caffeine (49.48%) 3. Ethanol (52.14%) Therefore, the order of increasing mass percent of carbon is: Sucrose, Caffeine, and Ethanol.

Key concepts

Chemical Composition

Understanding the chemical composition of a substance is fundamental in chemistry. It can be described as the identity, and the proportion, of the elements that make up a chemical compound. Each element within a compound is represented by a chemical symbol, such as C for carbon, H for hydrogen, and O for oxygen, often taken from the periodic table. For instance, the compound caffeine has the formula \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2}\), indicating it contains carbon, hydrogen, nitrogen, and oxygen in specific ratios.

When discussing chemical compounds purely by their element constituents, it’s essential to consider how much of each element contributes to the overall mass. This is what gives rise to concepts like the mass percent of carbon in a compound. By identifying the proportion of each element, one can gain insight into the compound's properties, reactivity, and potential applications in various fields like medicine or manufacturing.

Molar Mass Calculation

The molar mass calculation is a vital step when understanding the composition of a compound. It is the sum of the atomic masses of all atoms in a molecule and is typically expressed in grams per mole (g/mol).

To calculate the molar mass of a compound, one must start with the chemical formula and use the atomic masses of the elements involved (usually found on the periodic table). For example, looking at ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\), we calculate its molar mass by adding together the masses of two carbon atoms, six hydrogen atoms, and one oxygen atom:\[\mathrm{Molar\;mass\;of\;Ethanol} = (2 \times 12.01) + (6 \times 1.01) + (1 \times 16.00) = 46.07 \mathrm{g/mol}\].

Correct molar mass calculations are crucial for accurately determining the percent composition by mass and for various applications such as stoichiometric calculations in chemical reactions.

Percent Composition by Mass

The percent composition by mass is a measure of the concentration of a particular element within a chemical compound. It is defined as the mass of a given element divided by the total molar mass of the compound, multiplied by 100%. This concept allows chemists to determine the percentage of each element contained within a compound, enabling deeper insight into the compound's chemical behavior and how it may interact with other substances.

For example, to find the mass percent of carbon in sucrose, with its formula \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\), we would calculate the total mass of carbon (which is 12 atoms of carbon multiplied by the atomic mass of carbon) and then divide by the molar mass of sucrose we have previously calculated. Multiplying this ratio by 100% gives us the mass percent of carbon in sucrose:\[\mathrm{Mass\;percent\;of\;carbon} = \left( \frac{12 \times 12.01}{342.30} \right) \times 100\% \approx 42.11\%\].

Understanding and calculating percent composition by mass is essential not only for academic exercises but also for practical applications in chemistry, such as formulating pharmaceuticals or composites materials, where precise composition can affect overall product efficacy and quality.