Energy Transfer Efficiency: Glucose to Lactic Acid

This solution details the calculation for the efficiency of energy transfer when glucose is converted into lactic acid, utilizing the provided thermodynamic data.

Determine Total Energy Released

The primary energy source in this conversion is the free energy change ($∆G^0$) associated with transforming glucose into lactic acid.

• Given standard free energy change: $∆G^0_{glucose \to lactate} = -47000 \text{ cal/mol}$
• Converting to kilocalories per mole: $∆G^0_{glucose \to lactate} = -47 \text{ kcal/mol}$

This negative value signifies an exergonic reaction, releasing usable energy.

Calculate Energy Captured in ATP

The energy released by glucose conversion is partially captured to synthesize ATP from ADP and Pi. The efficiency depends on how much energy is stored in the newly formed ATP molecules.

• The provided equation shows that 2 moles of ATP are generated for every mole of glucose converted.
• The standard free energy change for ATP hydrolysis ($∆G^0_{ATP \ hydrolysis}$) is -7.3 kcal/mol. This value indicates the energy released when ATP is broken down, and conversely, the energy required to synthesize ATP from ADP and Pi.
• Energy captured = (Number of ATP molecules produced) $\times$ (Energy required per ATP molecule)
• Energy captured = $2 \times |∆G^0_{ATP \ hydrolysis}|$
• Energy captured = $2 \times |-7.3 \text{ kcal/mol}| = 2 \times 7.3 \text{ kcal/mol} = 14.6 \text{ kcal/mol}$

Compute Energy Transfer Efficiency

Energy transfer efficiency is calculated as the ratio of the energy successfully stored in ATP to the total energy made available by the glucose conversion, expressed as a percentage.

• Efficiency $= \left( \frac{\text{Energy Captured}}{\text{Total Energy Released}} \right) \times 100\%$
• Substituting the calculated values: Efficiency $= \left( \frac{14.6 \text{ kcal/mol}}{47 \text{ kcal/mol}} \right) \times 100\%$
• Calculating the ratio: Efficiency $= \left( \frac{14.6}{47} \right) \times 100\% \approx 0.310638 \times 100\%$
• This results in approximately $31.0638\%$.

Final Answer Rounding

The question requires the efficiency to be reported up to one decimal point.

• Rounding $31.0638\%$ to one decimal place gives $31.1\%$.