Question

Capsaicin is the compound that makes hot peppers spicy. This compound reversibly binds to the same protein that detects heat in our bodies. For that reason, when we eat spicy food we experience a “burning” sensation. The spice level in different types of peppers is measured in Scoville units. A Scoville unit refers to the number of times a pepper extract has to be diluted in order for a panel of people to no longer detect the heat. For example, a Jalapeño pepper ranks about ~5000 units. This means that liquid extracted from a Jalapeño must be diluted 5000 times before the heat is no longer detectable to the palate.

The spiciest peppers known, such as the Carolina Reaper, have about 3 million Scoville units of heat. Imagine you watch a show on TV claiming that the Carolina Reaper pepper is 600 times spicier than a Jalapeño (3 million divided by 5 thousand), since you know the thermodynamics of chemical equilibria, you can make a more nuanced assessment of that claim.

Explain why or why not the TV host above might or might not be correct. Clearly state any assumptions and use equations if necessary.

Answer 1

This question tries to test the concept behind dilution. Let us try to qualitatively analyze the scenario given.

We are told that 'hotness' of a chilly is measured in terms of Scoville units. Now the methodology adopted is diluting the chilly extract TILL everyone in a panel cant feel the 'heat' of the chilly extract. What this means is that the amount of capsaicin present in the diluted solution is so low that the protein that binds to capsaicin , cant really bind to it at this low concentration.

Reactions can be qualitatively gauged by the amounts of reactants in the solution. If more the reactants , we can expect a faster binding with the protein. At such low concentration of capsaicin, the reaction occurs too slowly for the body to detect.

Now, the TV show host claims that a certain type of chilly is x times "hotter" than Jalapeno. Before we dissect this claim, we must note that dilution of 500 implies 1ml of a solution is mixed with 499ml of pure water to make up 500ml of the 'diluted' solution.

The host claims that Carolina Reaper is 600 times hotter than Jalapeno. We know the Scoville units of Jalapeno is 5000 units.

600 times hotter implies we dilute the solution of Carolina Reaper 600 times more than what is required for Jalapeno. Which mathematically is 5000units * 600 = 3million units. The math works out!!!.

The claim made by the host is completely true.

Let us study the situation in a more detailed way.

Lets assume the reaction between the capsaicin and the receptor protein is as given below: (NOTE: the equation is in equilibrium)

. We further make an assumption that the body detects

the [bound complex] formed, with a certain sensitivity. What we mean by this is that the body registers the 'hotness' of a chilly only if a certain threshold of concentration (of [Bound Complex]) is achieved.

Remember that the Equilibrium constant of this reaction is defined as :

. We can find out the concentration of the [Bound Complex] if we are given with the value of K.

But, for any reaction, given certain physical parameters like the Temperature, Volume etc, the K for the reaction stays a constant. Which means that the changes that happen in the reaction are reflected in the concentration of the reacting species.

Now in the situation being described, we can determine the concentration of [Receptors] on an average. The concentration of [Capsaicin] is manually being regulated. We can empirically find out the value of K by performing the reaction with varied concentrations of [Capsaicin].

Now, based on the preceding discussion, we can safely say that we know the values of K, [Receptors] and [Capsaicin]. Using this we can find out the value of [Bound Complex] for every possible scenario.

The body will detect [Bound Complex] if and only if it finds that [Bound Complex] exceeds some threshold. This threshold is crossed after 1 unit Scoville.

I hope this has helped. In case you the answer is unclear, please do leave a comment. I will be more than glad to help you out.