Question

1. If a drug has an elimination rate constant of 0.564 hr-1, what is half life?
2. If 500mg of drug x is administered by iv bolus and result an initial plasma concentration of 120 mg/l.
The volume of distribution is?

Answer 1

To answer your questions, we can use the formulas associated with pharmacokinetics.

1. **Calculating Half-Life (t½):**

The half-life of a drug can be calculated using the elimination rate constant (k) with the following formula:

\[
t_{1/2} = \frac{0.693}{k}
\]

Where \(k\) is the elimination rate constant. Given \(k = 0.564 \, \text{hr}^{-1}\):

\[
t_{1/2} = \frac{0.693}{0.564} \approx 1.23 \, \text{hours}
\]

So, the half-life of the drug is approximately **1.23 hours**.

2. **Calculating Volume of Distribution (Vd):**

The volume of distribution (Vd) can be calculated using the initial plasma concentration and the amount of drug administered using the following formula:

\[
V_d = \frac{D}{C_0}
\]

Where:
- \(D\) = dose of the drug (in mg)
- \(C_0\) = initial plasma concentration (in mg/L)

Given:
- \(D = 500\, \text{mg}\)
- \(C_0 = 120\, \text{mg/L}\)

Now we can plug in the values:

\[
V_d = \frac{500 \, \text{mg}}{120 \, \text{mg/L}} \approx 4.17 \, \text{L}
\]

So, the volume of distribution of drug X is approximately **4.17 liters**.