Question

Calculate Approximately 38 mol of ATP are formed when glucose is completely oxidized during cellular respiration. If the heat of combustion for 1 mol of glucose is \(2.82 \times 10^{3} kJ / mol\) and each mole of ATP stores 30.5 \(kJ\) of energy, what is the efficiency of cellular respiration in terms of the percentage of available energy that is stored in the chemical bonds of ATP?

Short answer

The efficiency of cellular respiration in terms of the percentage of available energy stored in ATP is approximately \(41.13\%\).

Step-by-step solution

Calculate the total energy produced during the oxidation of 1 mol of glucose

Given that the heat of combustion for 1 mol of glucose is \(2.82 \times 10^3 kJ/mol\), the total energy produced during the oxidation of 1 mol of glucose can be represented as \(E_{glucose} = 2.82 \times 10^3 kJ/mol\).

Calculate the total energy stored in ATP molecules

We are given that 38 moles of ATP are formed during the complete oxidation of glucose, and each mole of ATP stores 30.5 kJ of energy. Therefore, the total energy stored in the 38 moles of ATP can be calculated as \(E_{ATP} = 38 \ mol \times 30.5\frac{kJ}{mol}\)

Compute the efficiency of cellular respiration in percentage

Now that we have the total energy produced during the oxidation of glucose and the total energy stored in the ATP molecules generated, we can calculate the efficiency of cellular respiration. The efficiency is calculated as the ratio of energy stored in ATP to the total energy generated during glucose oxidation, multiplied by 100 to express it as a percentage: \[\%Efficiency = \frac{E_{ATP}}{E_{glucose}} \times 100\] Substitute the values of \(E_{ATP}\) and \(E_{glucose}\) from Steps 1 and 2 into the formula and compute the efficiency.

Simplify the efficiency equation and compute the result

Now, we can simplify the equation from Step 3 and compute the efficiency. \[\%Efficiency = \frac{38 \ mol \times 30.5\frac{kJ}{mol}}{2.82 \times 10^3 kJ/mol} \times 100\] \[\%Efficiency = \frac{1159 kJ}{2.82 \times 10^3 kJ/mol} \times 100\] \[\%Efficiency \approx 41.13\%\] Therefore, the efficiency of cellular respiration in terms of the percentage of available energy stored in ATP is approximately 41.13%.

Key concepts

ATP Energy Storage

Adenosine Triphosphate, or ATP for short, is like a tiny battery that stores energy cells need to perform work. Think of it as a chemical currency used by our cells. Each molecule of ATP can store energy, which can then be used for various cellular activities.
The energy gets stored in the bonds of the phosphate groups. When one of those bonds is broken, energy is released, and a phosphate group is removed. This process transforms ATP into ADP (adenosine diphosphate). The cell can then use this released energy for important functions like muscle contraction or nerve impulse propagation.
In terms of quantity, one mole of ATP stores about 30.5 kJ of energy. Hence, when cells make a lot of ATP, they can store a significant amount of energy, ready to power cellular processes as needed.

Heat of Combustion

The heat of combustion is a measure of how much energy is released when a substance is completely burned. For glucose, this involves its oxidation, or reaction with oxygen, leading to energy release. In our context, this value is roughly 2820 kJ for each mole of glucose.
This energy is typically released as heat, which is why the term is called "heat" of combustion. In cellular respiration, instead of burning the glucose all at once and releasing heat, the cell slowly extracts energy in a more controlled fashion, capturing it in the form of ATP.
This process allows living organisms to harness energy efficiently, providing the necessary levels of energy to thrive and perform all cellular activities. Without efficient energy release seen with glucose combustion, cells would be unoriented in energy usage.

Glucose Oxidation

Glucose oxidation refers to the biochemical process where glucose is broken down to carbon dioxide and water, releasing energy. This transformation happens in the cell's mitochondria through a series of reactions known as cellular respiration.
The primary aim of glucose oxidation is to convert the chemical energy stored in glucose into ATP. For each mole of glucose oxidized, about 38 moles of ATP are produced, along with water and carbon dioxide as byproducts.
The controlled steps of glucose oxidation ensure that the energy in glucose is efficiently transformed into useful energy forms, rather than being wasted as heat. By doing so, cells can maximize the energy extracted from glucose, allowing for efficient biological processes.

Chemical Energy Conversion

Chemical energy conversion is a fascinating process where the energy stored in chemical bonds is transformed into different forms that cells can utilize. In cellular respiration, glucose serves as the primary source of chemical energy.
Through various stages including glycolysis, the Krebs cycle, and the electron transport chain, the energy from glucose molecules is converted into ATP molecules. This conversion ensures that energy from complex compounds like glucose is systematically broken down and stored in simpler, more stable molecules of ATP.
The efficiency of this conversion process is notable, as it allows the utilization of up to 41.13% of the energy from glucose in the formation of ATP, highlighting the sophisticated energy management in living cells. This balance between energy input and output is crucial to sustain life on a cellular level.