Animals operate under conditons of constant pressure and most of the process tht maintain life are isothermal ( in a broad sense) . How much energy is available for sustaining this type of muscular and nervous activity from the combustion of 1mol of glucose molecules under standard conditons at `37^(@)` C (blood temperature) ? The entropy change is `+182.4 JK^(-1)` for the reaction stated above
`DeltaH_("combustion")`[glucose]=-2808 KJ

Options

A. `-2754.4` kJ
B. `-2864.5` kJ
C. `-56.5` kJ
D. `-2808` kJ

Explanation

To solve the problem, we need to calculate the Gibbs free energy change (ΔG) for the combustion of glucose at a temperature of 37°C. We will use the formula:

\[ \Delta G = \Delta H - T \Delta S \]

### Step-by-Step Solution

**Step 1: Convert the temperature from Celsius to Kelvin.**
- Given temperature = 37°C
- To convert to Kelvin, use the formula:
\[ T(K) = T(°C) + 273 \]
\[ T = 37 + 273 = 310 \text{ K} \]

**Step 2: Identify the given values.**
- ΔH (enthalpy change for combustion of glucose) = -2808 kJ
- ΔS (entropy change) = +182.4 J/K

**Step 3: Convert ΔS from J/K to kJ/K.**
- Since ΔH is in kJ, we need to convert ΔS to the same unit:
\[ \Delta S = 182.4 \text{ J/K} = \frac{182.4}{1000} \text{ kJ/K} = 0.1824 \text{ kJ/K} \]

**Step 4: Substitute the values into the Gibbs free energy formula.**
\[ \Delta G = \Delta H - T \Delta S \]
Substituting the known values:
\[ \Delta G = -2808 \text{ kJ} - (310 \text{ K} \times 0.1824 \text{ kJ/K}) \]

**Step 5: Calculate the product of T and ΔS.**
\[ T \Delta S = 310 \times 0.1824 = 56.544 \text{ kJ} \]

**Step 6: Substitute this value back into the equation for ΔG.**
\[ \Delta G = -2808 \text{ kJ} - 56.544 \text{ kJ} \]
\[ \Delta G = -2864.544 \text{ kJ} \]

**Step 7: Round the result to an appropriate number of significant figures.**
\[ \Delta G \approx -2864.5 \text{ kJ} \]

### Final Answer
The energy available for sustaining muscular and nervous activity from the combustion of 1 mole of glucose under standard conditions at 37°C is approximately **-2864.5 kJ**.