Question

question 9
0/1 pt 5 19 details
when equal masses of the following compounds undergoes complete combustion, which chemicals will produce the least co₂?
4-greatest
2
3
1-least
subn estion
a. benzene, c₆h₆
b. glucose, c₆h₁₂o₆
c. cyclohexane, c₆h₁₂
d. methane, ch₄

Explanation:

Step 1: Understand the key concept

To determine which compound produces the least \( \text{CO}_2 \) upon complete combustion with equal masses, we need to consider the mass fraction of carbon in each compound. The lower the mass fraction of carbon, the less \( \text{CO}_2 \) will be produced (since \( \text{CO}_2 \) comes from the carbon in the compound). The formula for the mass fraction of carbon (\( w_C \)) in a compound with molecular formula \( \text{C}_x\text{H}_y\text{O}_z \) is \( w_C=\frac{x\times M_C}{M_{\text{molar}}} \), where \( M_C = 12\space\text{g/mol} \) and \( M_{\text{molar}} \) is the molar mass of the compound.

Step 2: Calculate molar mass and carbon mass fraction for each compound

• Benzene (\( \text{C}_6\text{H}_6 \)):

Molar mass \( M = 6\times12 + 6\times1=78\space\text{g/mol} \)
Mass of carbon \( m_C=6\times12 = 72\space\text{g/mol} \)
Mass fraction of carbon \( w_C=\frac{72}{78}\approx0.923 \)

• Glucose (\( \text{C}_6\text{H}_{12}\text{O}_6 \)):

Molar mass \( M = 6\times12+12\times1 + 6\times16=180\space\text{g/mol} \)
Mass of carbon \( m_C = 6\times12=72\space\text{g/mol} \)
Mass fraction of carbon \( w_C=\frac{72}{180} = 0.4 \)

• Cyclohexane (\( \text{C}_6\text{H}_{12} \)):

Molar mass \( M=6\times12 + 12\times1 = 84\space\text{g/mol} \)
Mass of carbon \( m_C=6\times12 = 72\space\text{g/mol} \)
Mass fraction of carbon \( w_C=\frac{72}{84}\approx0.857 \)

• Methane (\( \text{CH}_4 \)):

Molar mass \( M=12 + 4\times1=16\space\text{g/mol} \)
Mass of carbon \( m_C = 12\space\text{g/mol} \)
Mass fraction of carbon \( w_C=\frac{12}{16}=0.75 \)

Step 3: Compare the carbon mass fractions

We have the carbon mass fractions:

• Benzene: \( \approx0.923 \)
• Glucose: \( 0.4 \)
• Cyclohexane: \( \approx0.857 \)
• Methane: \( 0.75 \)

The lowest carbon mass fraction is in glucose (\( \text{C}_6\text{H}_{12}\text{O}_6 \)) because \( 0.4 \) is less than \( 0.75 \), \( 0.857 \), and \( 0.923 \).

Answer:

b. Glucose, \( \text{C}_6\text{H}_{12}\text{O}_6 \)