During strenuous exercise, GLUT4 will be active to bring glucose into the cell. Glucose is then pushed through glycolysis to generate pyruvate. Pyruvate is then pushed through pyruvate dehydrogenase complex, where it is converted into acetyl-CoA, which feeds into the Krebs cycle (assuming aerobic conditions) to generate ATP, NADH, , and carbon dioxide.  

Most of the intermediate molecules in the Krebs cycle can, rather than continuing through the cycle itself, go through other pathways to form macromolecules. Citrate can be used to create fatty acids and sterols. Alph-ketoglutarate can be used to make some of the amino acids. Succinyl-CoA can be used to make porphyrins, heme, and chlorophyll. Aspartate can be used to make some of the amino acids. Oxaloacetate can be used in gluconeogenesis to create glucose.

The citric acid cycle intermediate, fumarate, contains four atoms of carbon.

As a frame of reference, one molecule of glucose, the starting material for glycolysis, contains six atoms of carbon. The carbohydrate products of glycolysis are two molecules of pyruvate, with one molecule of pyruvate containing three atoms of carbon.

In preparation for entering the citric acid cycle, pyruvate loses one molecule of carbon dioxide, and therefore one molecule of carbon, to form acetyl-CoA, which contains two atoms of carbon. Acetyl-CoA is then combined with a molecule of oxaloacetate, which contains four atoms of carbon, to produce a molecule of citrate, which contains six atoms of carbon, and is the starting point for the citric acid cycle.

Citrate undergoes a number of a reactions, via the citric acid cycle, most notably two reactions in which a single molecule of carbon dioxide, and therefore carbon, is lost, thereby decreasing the total number of carbons to four atoms. The two reactions that remove carbons are the conversion of isocitrate to alpha-ketoglutarate and the conversion of alpha-ketoglutarate to succinyl-CoA. No additional carbons are removed prior to the production of fumarate, and therefore, fumarate contains four atoms of carbon. 

The citric acid cycle intermediate, malate, contains four atoms of carbon.

A single glucose molecule, which is the starting material for glycolysis, contains six carbon atoms. Glycolysis produces two pyruvate molecules, and one pyruvate molecule contains three carbon atoms.

Prior to entering the citric acid cycle, pyruvate loses one carbon dioxide molecule (e.g. one carbon atom), forming acetyl-CoA, which contains two carbon atoms. Acetyl-CoA then combines with one oxaloacetate molecule, a four-carbon molecule, to produce a molecule of citrate, which contains six carbon atoms, and is the starting material for the citric acid cycle.

Citrate undergoes a number of a reactions in the citric acid cycle, including two reactions where one atom of carbon dioxide (e.g. carbon) is lost, which decreases the total number of carbons to four atoms. The two reactions that remove carbons are the conversion of isocitrate to alpha-ketoglutarate and the conversion of alpha-ketoglutarate to succinyl-CoA. No additional carbons are removed prior to the production of malate. Therefore, malate contains four atoms of carbon. 

Acetyl-CoA is not part of the cycle but is oxidized by it. There are two decarboxylations in the cycle, from isocitrate to alpha-ketoglutarate, and from alpha-ketoglutarate to succinyl-CoA. In total, three equivalents of  are produced in the cycle. Isocitrate is a compound in the cycle, produced from citrate.

Even though an  is generated when malate is dehydrogenated to oxaloacetate, this oxidation is very unfavorable because of the addition of a reactive ketone in place of an alcohol on the 2nd carbon. In fact, the only way this reaction can proceed is if oxaloacetate concentration is very low. All of the other reactions have large negative  values.

The formation of alpha-ketoglutarate from isocitrate using the enzyme alpha-ketoglutarate dehydrogenase is an irreversible reaction due to its largely negative  value.

This question is providing us with a scenario in which  ions enter a cell. We're further told that it will take a single molecule of ATP to move three of these ions out of the cell. Finally, we are being asked to determine the total number of acetyl-CoA molecules that must pass through the Krebs cycle in order to provide the energy necessary for the export of these  ions.

First, we'll need to determine the total number of ATP molecules generated from the passage of a single molecule of acetyl-CoA through the Krebs cycle. It's important to remember that the passage of acetyl-CoA through the Krebs cycle generates one molecule of ATP directly by substrate-level phosphorylation, but it also produces other intermediate energy carriers in the form of  and .

For each acetyl-CoA ran through the cycle, one molecule of  and three molecules of  are produced. Furthermore, each molecule of  will go on to donate its electrons to the electron transport chain to generate  molecules of ATP per molecule of  oxidized. Likewise, each  will also produce ATP via oxidative phosphorylation, but at a rate of  molecules of ATP per molecule of  oxidized.

Adding these up, we obtain:

 ATP via substrate-level phosphorylation

Adding these values up, we have a total of  molecules of ATP produced for every molecule of acetyl-CoA oxidized. Now that we know how much ATP is produced from one acetyl-CoA, we can calculate the number needed to move the  ions out of the cell.

The only step of the citric acid cycle (also known as the Krebs cycle, or the TCA cycle) that directly produces ATP or GTP is the conversion of succinyl-CoA to succinate. 

In this reaction, succinyl-CoA is converted to succinate with the assistance of the enzyme, succinyl-CoA synthetase. During this reaction, ADP + Pi (or GDP + Pi) is also converted to ATP (or GTP) using the energy from the breaking of the bond between CoA and succinate. Thus, the overall reaction appears as:

While side products of some of the other reactions listed produce intermediaries that may be used to produce ATP in the future, these reactions do not directly produce ATP.

The only citric acid cycle (also known as the Krebs cycle or TCA cycle) step listed that does not result in the production of  as a side product is the conversion of fumarate to malate. 

In the conversion of fumarate to malate, fumarate is chemically combined with water in the presence of the enzyme fumarase to produce malate. In this conversion, there is no concomitant production of .

In each of the other reactions listed,  is converted to  and  as side products.