Question

we want to determine how many molecules of c₁₂h₂₂o₁₁ are present when a sample of sucrose has 3.6 x 10²⁴ atoms c. what is the missing conversion factor? 3.6 x 10²⁴ atoms c ? / ? 6.02 x 10²³ mlc c₁₂h₂₂o₁₁ / 12 atom c; 1 mlc c₁₂h₂₂o₁₁ / 12 atom c; 12 mol c / 1 mol c₁₂h₂₂o₁₁

Explanation:

Step1: Analyze the formula of sucrose

The formula for sucrose is \( C_{12}H_{22}O_{11} \), which means that in one molecule of sucrose, there are 12 atoms of carbon. So, to convert from the number of carbon atoms to the number of sucrose molecules, we need a conversion factor that relates the number of carbon atoms to the number of sucrose molecules.

Step2: Evaluate the conversion factors

• The first option: \( \frac{6.02\times 10^{23}\text{ mlc }C_{12}H_{22}O_{11}}{12\text{ atom }C} \) - This involves Avogadro's number, but we don't need Avogadro's number here because we are converting from carbon atoms to sucrose molecules directly using the ratio from the formula.
• The second option: \( \frac{1\text{ mlc }C_{12}H_{22}O_{11}}{12\text{ atom }C} \) - Since 1 molecule of sucrose has 12 carbon atoms, this conversion factor correctly relates the number of carbon atoms to the number of sucrose molecules. For every 12 carbon atoms, we have 1 molecule of sucrose.
• The third option: \( \frac{12\text{ mol }C}{1\text{ mol }C_{12}H_{22}O_{11}} \) - This is a molar ratio, but the question is about converting from atoms of C to molecules of sucrose, not moles. So this is not the correct conversion factor here.

Answer:

B. \( \frac{1\text{ mlc }C_{12}H_{22}O_{11}}{12\text{ atom }C} \)