What's In Your Sports Drink?

ACCM Concepts:

• VIII. D. 1. a. Reactions with very small values of K will have little formation of products, while reactions with very large values of K will proceed nearly completely to products.

• VIII. D. 2. a. Strong acids have very large K values and are considered fully ionized; weak acids have small K values and are only partially ionized.

Introduction

Growing up, many of us have likely been exposed to sports drinks such as Gatorade or rehydration drinks such as Pedialyte. Whether it be after a sports event, when feeling dehydrated, or feeling stomach pain, these drinks serve as sources of rehydration through providing electrolytes. 

Intro To Equilibrium

In examining these drinks, we can also think about the ways equilibrium intertwines with the presence of electrolytes. Before looking at electrolytes, we must establish equilibrium. In a chemical reaction, we often witness the forward reaction and its rate of change. This is where the reactants produce products. However, reactions are reversible to some extent, where an opposing reaction occurs in which products react to form the reactants. As with the forward reaction, the reverse reaction also has a rate of change. Equilibrium is reached when the forward reaction rate equals the reverse reaction rate (8).

The equilibrium constant, K, gives us a ratio of the forward reaction rate to the reverse reaction rate. In the reaction, aA ⇆ bB, \(K=\frac{[B]^b}{[A]^a}\), where [A] refers to the concentration of A and [B] to the concentration of B. When K >> 1, one can see that the equilibrium concentration of products is greater than that of reactants. On the contrary, when K << 1, the equilibrium concentration of reactants is greater than that of products (9).

Strong vs. Weak Electrolytes

Electrolytes are substances that “give ions when dissolved in water” (2). They are not limited to salts, but also include acids and bases. Within the umbrella of electrolytes, there are strong and weak electrolytes. Strong electrolytes “completely ionize when dissolved” (2). One example of a salt that is a strong electrolyte is KBr. It’s dissolution is represented by the following equation:

\[KBr(s) → K^+(aq) + Br^-(aq) \nonumber\]

 

Some other examples of strong electrolytes include salts such as NaCl, strong acids such as HBr, and strong bases such as NaOH. On the contrary, for a weak electrolyte, a “small fraction of [its] molecules ionize when dissolved in water” (2). Some examples include acids such as citric acid and bases such as ammonia. We also use the equilibrium constant, K, in order to denote ionization for the ionization of a weak electrolyte (2). More specifically, we can use the solubility constant, \(K_{sp}\), to analyze the dissolution of a solid. When \(K_{sp}\) is large, the solid is more soluble (10). Pointing back to the aforementioned dissolution, \(K_{sp}=[K+][Br-]\). The solid KBr is not present in the expression because we don’t include solids in equilibrium constant expressions (10).

 

Gatorade’s active ingredients include Sodium Citrate and Monopotassium Phosphate. The former dissolves in water to produce Sodium and Citrate. The following equation shows its dissolution:

\[Na_3C_6H_5O_7(s) → 3Na^+(aq) + C_6H_5O_7^{3-}(aq)\nonumber\]

Sodium is a strong electrolyte which is essential in Gatorade due to its vital role within the body. It’s the most abundant electrolyte in the body and has many important functions (3). Humans require only about 1-2mm per day, but since our typical diet is so considerably greater than this, (130-160mmol/day), it’s often filtered by our kidneys and filtered out though our urine (4). This overly excess sodium is often a cause of high blood pressure in individuals. When consumed appropriately, sodium is a critical electrolyte that helps your cells maintain appropriate balance of fluids. 

Citrate, however, is a weak base (and weak electrolyte) and when it dissolves in water, its dissolution is given by the following equation:

\[C_6H_5O_7^{3-}(aq) + H_2O(l) ⇆ OH^-(aq) + HC_6H_5O_7^{2-}(aq)\nonumber\]

On the other hand, Monopotassium Phosphate dissolves in water to produce Potassium and Phosphoric Acid. The following equation shows its dissolution:

\[KH_2PO_4(s) → K^+(aq) + H_2PO_4^-(aq)\nonumber\]

Potassium is another important electrolyte that is used in conjunction with sodium. Its primary purpose is to “establish the resting membrane potential in neurons and muscle fibers after membrane depolarization and action potentials.” (4).....Potassium is also very important for your heart, and improper balances of it can cause serious heart issues. 

Phosphoric Acid, however, is a weak acid (and weak electrolyte) and when it dissolves in water, its dissolution is given by the following equation:

\[H_2PO_4^-(aq) + H_2O (l) ⇆ H_3O^+(aq) + HPO_4^{2-}(aq)\nonumber\]

 

Example \(\PageIndex{1}\)

Let's suppose a 1 L bottle of Gatorade containing 0.0032 M Monopotassium Phosphate. The \(K_a\) of \(H_2PO_4^-\) is \(6.2x10^{-8}\) Using this information and its dissolution, calculate the equilibrium concentration of \(HPO_4^{2-}\).

Solution

Because we have Monopotassium Phosphate, which dissolves into Potassium and Phosphoric Acid, we can use its dissolution to calculate the amount of Phosphoric Acid in solution.

\[KH_2PO_4(s) → K^+(aq) + H_2PO_4^-(aq)\nonumber\]

Due to the 1:1 stoichiometric ratio between \(HPO_4^{2-}\) and \(KH_2PO_4\), we know that the moles of \(KH_2PO_4\) = moles of \(HPO_4^{2-}\). Thereafter, we can use the reaction of \(KH_2PO_4\) and water to determine how much \(HPO_4^{2-}\) is produced.

\[H_2PO_4^-(aq) + H_2O (l) ⇆ H_3O^+(aq) + HPO_4^{2-}(aq)\nonumber\]

Now, we can set up an ICE (Initial, Change, and Equilibrium) table to calculate the equilibrium concentration of \(HPO_4^{2-}\):

Reaction Progress:	\(H_2PO_4^-\)	\(H_2O\)	\(H_3O^+\)	\(HPO_4^{2-}\)
Initial	0.0032 M	Ignore	0 M	0 M
Change	- x	Ignore	+ x	+ x
Equilibrium	0.0032 - x	Ignore	x	x

We can then solve for [\(HPO_4^{2-}\)]:

\[6.2x10^{-8}=\frac{x^2}{0.0032-x}\nonumber\]

\[x^2=(6.2 x 10^{-8})(0.0032-x)\nonumber\]

\[x=[HPO_4^{2-}]=1.41x10^{-5} M\]

Thus, the concentration of \(HPO_4^{2-}\) is \(1.41x10^{-5} M\).

Acidic and Basic Electrolytes

Moreover, we can also use \(K_a\) to look at the acidic and basic electrolytes. For example, hydrofluoric acid, HF, has a \(K_a\) of 6.6 x \(10^{-4}\). It’s reaction with water is given by the following equation:

\[HF(aq) + H_2O (l) ⇆ H_3O^+(aq) + F^-(aq) \nonumber\]

Thus, it’s equilibrium constant, \(K_a\), is defined as:

\[K_a= \frac{[H_3O^+][F^-]}{[HF]} \nonumber\]

 

Example \(\PageIndex{2}\)

Gatorade has Citric Acid, which is an example of a weak acid and thus a weak electrolyte. Benzoic Acid is also a weak acid with a \(K_a\) of 6.46x\(10^{-5}\). Find the pH of a 0.2 M solution of Benzoic Acid.

Solution

We have 0.2 M Benzoic Acid, and its dissociation in water is given by the following equation:

\[HC_7H_3O_2(aq) + H_2O (l) ⇆ H_3O^+(aq) + C_7H_3O_2^-(aq) \nonumber\]

Knowing this, we need to set up an ICE table in order to see how much \(H_3O^+\) is produced at equilibrium:

Reaction Progress:	\(HC_7H_3O_2\)	\(H_2O\)	\( H_3O^+\)	\(C_7H_3O_2^-\)
Initial	0.2 M	Ignore	0 M	0 M
Change	- x	Ignore	+ x	+ x
Equilibrium	0.2 - x	Ignore	x	x

To solve for the concentration of \( H_3O^+\), which is equal to x, we can use the following equation:

\[6.46 x 10^{-5}=\frac{x^2}{0.2-x}\nonumber\]

\[x^2=(6.46 x 10^{-5})(0.2-x)\nonumber\]

\[x=[H_3O^+]=3.56x10^{-3} M\]

Using the concentration of \( H_3O^+\), we can solve for the pH:

\[pH=-log[H_3O^+]=2.45\]

Conclusion

We can use this to find information about the weak acid, such as its pH at a given concentration or the amount of hydronium produced. Other uses of electrolytes are found in batteries or in other chemical reactions.

Within the body, electrolytes serve a pivotal role in helping the body maintain balance (3). They work to “transport chemical compounds in and out of cells” (3). The main electrolytes in the body fluid are known as macrominerals (2). Some examples include Sodium, Magnesium, Potassium, and Calcium (3). Too much or too little of these can lead to serious conditions, such as Hypokalemia which is due to not enough Potassium and causes muscle weakness (3). 

References:

1. Coombes, J.S., Hamilton, K.L. The Effectiveness of Commercially Available Sports Drinks. Sports Med 29, 181–209 (2000). DOI: https://doi.org/10.2165/00007256-200029030-00004

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3. Electrolytes https://my.clevelandclinic.org/health/diagnostics/21790-electrolytes (accessed Nov 9, 2022)

4. Electrolyte Balance https://bio.libretexts.org/@go/page/34668 (accessed Nov 9, 2022).

5. Moore, Justin Shorb, Xavier Prat-Resina, Tim Wendorff, E. V., John W.; Hahn, A. Osmotic Pressure https://chem.libretexts.org/@go/page/49680 (accessed Nov 9, 2022).

6. Osmoregulation and Osmotic Balance - Transport of Electrolytes across Cell Membranes https://bio.libretexts.org/@go/page/14064 (accessed Nov 11, 2022).

7. The Great Hydration Smackdown: Pedialyte vs. Gatorade. https://greatist.com/eat/pedialyte-vs-gatorade (accessed Nov 11, 2022)

8. The Concept of Equilibrium https://chem.libretexts.org/@go/page/25167 (accessed Dec 5, 2022).

9. The Equilibrium Constant https://chem.libretexts.org/@go/page/25168 (accessed Dec 5, 2022).

10. Solubility Product Constant, Ksp https://chem.libretexts.org/@go/page/1614 (accessed Dec 5, 2022).