Combustion of glucose $\left( C _6 H _{12} O _6\right)$ is the main source of energy for animal cells:
$C_6 H_{12} O_6(s)+6 O_2(g) \rightarrow 6 CO_2(g)+6 H_2 O(l) \quad \Delta G_{r x n}\left(37{ }^{\circ} C\right)=-2872 . kJ$
This energy is generally stored as ATP (adenosine triphosphate) molecules, which can release it when convenient by hydrolysis ("water-assisted decomposition") into ADP (adenosine diphosphate) molecules and a phosphate anion, often given the symbol $P_i$ in biochemistry:
$\operatorname{ATP}(a q) \rightarrow \operatorname{ADP}(a q)+P_{i}(a q) \quad \Delta G_{r x n}=-35 \text { to } 70 kJ$
The actual amount of free energy released by the hydrolysis of ATP varies, depending on the exact conditions inside the cell.
Suppose under certain conditions hydrolysis of ATP actually releases $-64.3 kJ / mol$. Calculate the maximum number of ATPs that could be created from ADPs and $P_i$ by the combustion of a molecule of glucose. Your answer must be a whole number.
Answer (1)
The combustion of one glucose molecule releases 2872 kJ of energy.
The hydrolysis of one ATP molecule requires 64.3 kJ of energy.
Divide the total energy released by glucose combustion by the energy required for ATP hydrolysis: 64.3 2872 ≈ 44.67 .
Take the floor of the result to find the maximum number of ATP molecules: 44 .
Explanation
Understanding the Problem We are given that the combustion of one molecule of glucose releases 2872 kJ of energy. We are also given that the hydrolysis of one molecule of ATP releases 64.3 kJ of energy. We want to find the maximum number of ATP molecules that can be created from the energy released by the combustion of one molecule of glucose.
Setting up the Inequality Let n be the number of ATP molecules created. The total energy required to create n ATP molecules is n × 64.3 kJ . The energy released from the combustion of 1 mole of glucose is 2872 kJ. We need to find the maximum integer value of n such that the total energy required to create n ATP molecules is less than or equal to the energy released from the combustion of 1 mole of glucose.
Formulating the Inequality We can set up the inequality: n × 64.3 ≤ 2872
Solving for n To solve for n , we divide both sides of the inequality by 64.3: n ≤ 64.3 2872 n ≤ 44.6656298600311 Since n must be a whole number, we take the floor of the result: n = ⌊ 44.6656298600311 ⌋ = 44
Final Answer Therefore, the maximum number of ATP molecules that can be created from the combustion of one molecule of glucose is 44.
Examples
In the human body, the energy released from the food we eat, like glucose, is used to create ATP. ATP then acts as the energy currency of the cell, powering various biological processes such as muscle contraction, nerve impulse transmission, and protein synthesis. Understanding how many ATP molecules can be generated from a single glucose molecule helps scientists optimize metabolic pathways and develop strategies to improve energy efficiency in cells.
