Problem 79 - Chemistry Matter and Change

Question

Which law would you use to compare \(\mathrm{CO}\) and \(\mathrm{CO}_{2}\) ? Explain. Without doing any calculations, determine which of the two compounds has the highest percent by mass of oxygen in the compound.

Step-by-Step Solution

Answer

Use percent composition. CO₂ has a higher percent by mass of oxygen than CO.

Step 1: Identify Relevant Law

To compare the percent by mass of oxygen in two compounds, we can use the concept of molar mass and percent composition in Chemistry. Percent composition is often a technique for comparing different compounds composed of similar elements, such as oxygen in this case.

Step 2: Determine Molar Mass of Compounds

Calculate the molar mass of each compound. - For CO: The molar mass is the sum of the atomic masses of carbon (12 g/mol) and oxygen (16 g/mol), which gives a total molar mass of 28 g/mol. - For CO₂: The molar mass is the sum of the atomic mass of carbon (12 g/mol) and two oxygens (2 × 16 g/mol), which gives a total molar mass of 44 g/mol.

Step 3: Calculate Percent by Mass of Oxygen

Determine the percent by mass of oxygen in each compound:- For CO, the percent by mass of oxygen is: \[ \frac{16 \text{ g/mol (Oxygen)}}{28 \text{ g/mol (CO)}} \times 100 = 57.14\% \]- For CO₂, the percent by mass of oxygen is: \[ \frac{32 \text{ g/mol (Oxygen)}}{44 \text{ g/mol (CO₂)}} \times 100 = 72.73\% \]

Step 4: Compare Percentages

Compare the calculated percent by mass of oxygen between the two compounds: - CO has 57.14% by mass of oxygen. - CO₂ has 72.73% by mass of oxygen. Thus, CO₂ has a higher percent by mass of oxygen compared to CO.

Key Concepts

Molar Mass

Understanding molar mass is crucial in chemistry, as it forms the basis for comparing components of various compounds. Simply put, molar mass is the total mass of one mole of a given chemical substance. It's expressed in grams per mole (g/mol). Calculating the molar mass of a compound involves adding up the atomic masses of all the atoms present in the molecule. For instance, carbon monoxide (CO) consists of one carbon atom and one oxygen atom. The atomic mass of carbon is approximately 12 g/mol, and that of oxygen is approximately 16 g/mol. Therefore, the molar mass of CO is 12 + 16 = 28 g/mol. Similarly, carbon dioxide (CO₂) contains one carbon atom and two oxygen atoms. Therefore, its molar mass is 12 + (2 × 16) = 44 g/mol. Understanding these calculations is key to performing other analyses, such as chemical compound analysis and percent composition.

Chemical Compound Analysis

Chemical compound analysis is the process used to determine the composition of elements within a chemical substance. This process often involves calculating the percent composition of each element in the compound. By identifying the amount of each element present, chemists can better understand and compare different substances. When analyzing carbon monoxide (CO) and carbon dioxide (CO₂), knowing their molar masses helps chemists determine how much of the compound's mass comes from each element involved. For CO, the percent composition can be identified by dividing the atomic mass of oxygen (16 g/mol) by the total molar mass of CO (28 g/mol), resulting in about 57.14%. Similarly, for CO₂, the calculation involves dividing the combined atomic mass of two oxygens (32 g/mol) by the total molar mass of CO₂ (44 g/mol), resulting in about 72.73%. These calculations allow chemists to compare the oxygen content in both compounds.

Oxygen Content Analysis

Oxygen content analysis is an important aspect of understanding a compound's makeup and properties. This type of analysis looks specifically at how much of the compound's mass is made up of oxygen. To find the percent by mass of oxygen, we take the mass of oxygen in the compound and divide it by the compound's total molar mass, then multiply by 100 to convert it to a percentage.For example, in the compounds CO and CO₂, the process of oxygen content analysis helps to determine how oxygen-rich these compounds are. In CO, oxygen contributes about 57.14% to the total mass, as calculated using the formula: \[ \frac{16 \text{ g/mol (Oxygen)}}{28 \text{ g/mol (CO)}} \times 100 \approx 57.14\% \]In CO₂, the calculation reveals that oxygen makes up approximately 72.73% of the compound's total mass:\[ \frac{32 \text{ g/mol (Oxygen)}}{44 \text{ g/mol (CO₂)}} \times 100 \approx 72.73\% \]This analysis shows that CO₂ is richer in oxygen compared to CO, demonstrating how oxygen content analysis can effectively determine differences in composition between similar compounds.