Problem 72 - Chemistry Matter and Change

Question

a. What is the percent by mass of carbon in 44 \(g\) of carbon dioxide \(\left(CO_{2}\right) ?\) b. What is the percent by mass of oxygen in 44 \(g\) of carbon dioxide \(\left(CO_{2}\right)\) ?

Step-by-Step Solution

Answer

a. The percent by mass of carbon in 44 g of carbon dioxide \(CO_{2}\) is 27.27%. b. The percent by mass of oxygen in 44 g of carbon dioxide \(CO_{2}\) is 72.73%.

Step 1: Determine the molar mass of CO₂

Using the periodic table, the molar masses of carbon (C) and oxygen (O) can be found: - Molar mass of Carbon (C) = 12.01 g/mol - Molar mass of Oxygen (O) = 16.00 g/mol As there are two oxygen atoms in the CO₂ molecule, we should multiply the molar mass of oxygen by 2 and then add the molar mass of carbon to find the molar mass of the entire CO₂ molecule. Molar mass of CO₂ = Molar mass of C + 2 * Molar mass of O

Step 2: Calculate the molar mass of CO₂

Now, let's calculate the molar mass of CO₂ using the molar masses of C and O found earlier: Molar mass of CO₂ = (12.01 g/mol) + 2 * (16.00 g/mol) = 12.01 g/mol + 32.00 g/mol = 44.01 g/mol

Step 3: Calculate the mass percentages of C and O

To find the mass percentage of carbon (C) and oxygen (O) in one mole of CO₂, we will use the following formula: Percent by mass = (mass of element / molar mass of compound) * 100 a. Mass percentage of Carbon (C): Percentage of C in CO₂ = (12.01 g/mol / 44.01 g/mol) * 100 = 27.27 % b. Mass percentage of Oxygen (O): Percentage of O in CO₂ = (2 * 16 g/mol / 44.01 g/mol) * 100 = (32 g/mol / 44.01 g/mol) * 100 = 72.73 %

Step 4: Answer the questions

a. What is the percent by mass of carbon in 44 g of carbon dioxide (CO₂)? Percent by mass of Carbon = 27.27 % b. What is the percent by mass of oxygen in 44 g of carbon dioxide (CO₂)? Percent by mass of Oxygen = 72.73 %

Key Concepts

Molar Mass Calculation

Understanding the concept of molar mass is essential in stoichiometry. It helps you determine how much a substance weighs on a molecular level. To find the molar mass of a compound, like carbon dioxide (CO₂), you sum the molar masses of all the atoms present in one molecule of that compound.Here's how you do it:

• Identify the chemical formula of the compound, in this case, CO₂.
• Find the molar mass of each element from the periodic table. Carbon (C) has a molar mass of 12.01 g/mol, while Oxygen (O) has a molar mass of 16.00 g/mol.
• Multiply the molar mass of each element by the number of atoms of that element in one molecule of the compound. For CO₂, there is one carbon atom and two oxygen atoms, so we multiply: \[ \text{Molar mass of CO₂} = 12.01 \text{ g/mol} + (2 \times 16.00 \text{ g/mol}) \]
• Add these amounts together to find the total molar mass of the compound: 44.01 g/mol for CO₂.

Understanding molar mass allows us to connect macroscopic measurements to atomic-level quantities.

Percent Composition

The percent composition of a compound tells you the percentage by mass of each element within that compound. It offers insight into the proportion of elements and can help identify the compound.To calculate percent composition, use the formula:

• Find the molar mass of the compound, as we calculated earlier for CO₂, which is 44.01 g/mol.
• Find the mass contribution of each element in the compound. For carbon in CO₂, it is 12.01 g/mol, and for oxygen, it is \(2 \times 16.00 = 32.00\) g/mol.
• Use the equation \[ \text{Percent by mass} = \left( \frac{\text{mass of the element}}{\text{molar mass of compound}} \right) \times 100 \]
• For carbon: \[ \text{Percent of C} = \left( \frac{12.01}{44.01} \right) \times 100 = 27.27\% \]
• For oxygen: \[ \text{Percent of O} = \left( \frac{32.00}{44.01} \right) \times 100 = 72.73\% \]

This calculation helps chemists determine the makeup of a substance without needing to physically separate it into its constituent elements.

Chemical Formulas

Chemical formulas are like the recipes for molecules. They tell us which and how many atoms are linked together to create a molecule of a compound. For example, the chemical formula for carbon dioxide is CO₂, which tells us:

• There is one carbon atom (C) in each molecule of carbon dioxide.
• There are two oxygen atoms (O) in each molecule.

Chemical formulas serve several significant purposes:

• They provide a clear representation of the elemental structure of a compound.
• They help in calculating the molar mass of compounds by identifying the exact number of atoms of each element involved.
• They allow for the calculation of percent compositions, as done with CO₂.

By understanding chemical formulas, you can easily navigate tasks like calculating molar mass or percent composition, giving you a comprehensive understanding of the substances you're working with.