The enthalpy change involved in the oxidation of glucose is `-2880 kJ"mol"^(-1)`. Twenty five per cent of this energy is available for muscular work. If 100 kJ of muscular work is needed to walk one kilometer, what is the maximum distance that a person will be able to walk after eating 120 g of glucose?

Options

A. `4.8xx10^(4)`m
B. `4.8xx10^(3)`m
C. `4.8xx10^(5)`m
D. `4.8xx10^(2)`m

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the number of moles of glucose
The molar mass of glucose (C₆H₁₂O₆) is 180 g/mol. We need to find the number of moles in 120 g of glucose.

\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{120 \, \text{g}}{180 \, \text{g/mol}} = \frac{120}{180} = 0.67 \, \text{moles} \]

### Step 2: Calculate the total energy available for muscular work
The enthalpy change (ΔH) for the oxidation of glucose is given as -2880 kJ/mol. Since only 25% of this energy is available for muscular work, we can calculate the energy available for the moles of glucose consumed.

\[ \text{Energy available} = \text{Number of moles} \times \Delta H \times \text{Efficiency} \]

Where efficiency is 25%, or 0.25:

\[ \text{Energy available} = 0.67 \, \text{moles} \times (-2880 \, \text{kJ/mol}) \times 0.25 \]

Calculating this:

\[ \text{Energy available} = 0.67 \times -2880 \times 0.25 = -480 \, \text{kJ} \]

Since we are interested in the magnitude of energy available for work, we take the positive value:

\[ \text{Energy available} = 480 \, \text{kJ} \]

### Step 3: Calculate the maximum distance walked
We know that 100 kJ of muscular work is needed to walk 1 km. We can now find the maximum distance a person can walk with the available energy.

\[ \text{Distance} = \frac{\text{Energy available}}{\text{Energy needed per km}} = \frac{480 \, \text{kJ}}{100 \, \text{kJ/km}} \]

Calculating this gives:

\[ \text{Distance} = 4.8 \, \text{km} \]

### Final Answer
The maximum distance that a person will be able to walk after eating 120 g of glucose is **4.8 kilometers**.

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