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The problem asks for the correct differential equation that models a chemical reaction where the concentration \( H \) of a compound declines at a rate proportional to its concentration. The key phrase here is **"rate proportional to its concentration"**, which indicates that the rate of change of \( H \) with respect to time \( t \), i.e., \( \frac{dH}{dt} \), is proportional to \( H \).

### Understanding the Proportionality
In mathematical terms, if a quantity is decreasing at a rate proportional to its current value, the rate of change can be written as:
\[
\frac{dH}{dt} = -\gamma H
\]
where \( \gamma \) is a positive constant and the negative sign indicates that the concentration is decreasing.

### Correct Answer:
Thus, the correct option is:
\[
\boxed{\frac{dH}{dt} = -\gamma H}
\]
This option captures the idea that the concentration \( H \) declines over time at a rate proportional to \( H \).

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Would you like more details on this process, or have any other questions? Here are 5 follow-up questions that might interest you:

1. How do you solve this type of differential equation?
2. What does the solution to this differential equation look like?
3. How would the equation change if the concentration increased rather than decreased?
4. What does \( \gamma \) represent physically in this reaction?
5. How can you verify that a given differential equation models a real chemical reaction?

**Tip:** Always pay attention to whether a rate of change is proportional to the current value. This often leads to exponential growth or decay, modeled by differential equations like the one here.

A chemical reaction is taking place in a reaction vessel. One of the compounds in this reaction has concentration H in the reaction vessel where H is a function of time t. It is known that the concentration of this reactant declines at a rate proportional to its concentration. Which one of the differential equations below models the rate of change of the concentration of this reactant? You may assume that γ is a positive constant in each equation.

Explore how to model the rate of change in a chemical reaction where the concentration of a compound declines proportionally to its concentration. The differential equation dH/dt = -γH describes exponential decay, a key concept in differential equations and chemical kinetics.

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