**Core Concept**
The duration of action of intravenously administered drugs depends on various factors related to pharmacokinetics, including the drug's distribution, metabolism, and elimination. This concept is crucial in understanding how different drugs behave in the body and how to optimize their therapeutic effects.

**Why the Correct Answer is Right**
The correct answer is related to the drug's **volume of distribution (Vd)**. The volume of distribution is a pharmacokinetic parameter that predicts the extent to which a drug distributes from the plasma into the tissues. A high volume of distribution indicates that the drug is lipophilic and tends to distribute into body tissues, whereas a low volume of distribution indicates that the drug is hydrophilic and remains primarily in the bloodstream. As a result, drugs with a high volume of distribution tend to have a longer duration of action because they are more slowly eliminated from the body.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the **rate of administration** can affect the initial peak concentration of a drug, but it does not directly impact the duration of action.

**Option B:** This option is incorrect because **tissue binding** can affect the drug's distribution and elimination, but it is not the primary factor determining the duration of action of an intravenously administered drug.

**Option C:** This option is incorrect because **metabolism** and **elimination** are important factors in determining the duration of action of a drug, but they are not the primary factor being tested in this question.

**Clinical Pearl / High-Yield Fact**
A high volume of distribution is often associated with lipophilic drugs, which can be useful for achieving therapeutic effects in tissues with limited blood supply, such as the central nervous system.

**Correct Answer: C. Metabolism and elimination are the primary factors in determining the duration of action of an intravenously administered drug.