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The problem asks for the correct differential equation that models the rate of change of the concentration of a reactant \( H \) that declines at a constant rate. Here's a breakdown of the key concepts:

- \( H(t) \) is the concentration of the reactant as a function of time \( t \).
- The concentration declines at a constant rate, which means the rate of change of \( H \), or \( \frac{dH}{dt} \), must be negative because the concentration is decreasing over time.
- The rate is proportional to \( H \), meaning the change in concentration depends on the current amount of \( H \).

Given these clues, the correct equation is:

\[
\frac{dH}{dt} = -\gamma H
\]

This equation implies that the rate of change of the concentration is proportional to \( H \) and that it decreases over time (as shown by the negative sign). This matches the description that the concentration declines at a constant rate.

Thus, the correct answer is:

\[
\boxed{\frac{dH}{dt} = -\gamma H}
\]

Would you like further details on this? Here are some related questions you might explore:

1. What does the solution to the differential equation \( \frac{dH}{dt} = -\gamma H \) look like?
2. How does the constant \( \gamma \) affect the rate at which \( H \) declines?
3. What is the physical interpretation of \( \gamma \) in this context?
4. Can you explain how exponential decay relates to this differential equation?
5. How would the equation change if the concentration increased instead of decreased?

**Tip**: When analyzing problems involving rates of change, always carefully consider the sign of the rate to understand whether the quantity is increasing or decreasing.

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 constant rate. 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.

This problem models the concentration decline of a reactant in a chemical reaction using differential equations. The solution involves understanding exponential decay and the rate of change in concentration. Suitable for college-level students studying calculus or chemistry.

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