The rate at which a certain drug is eliminated by the body follows first-order kinetics, with a half life of 33 minutes. Suppose in a particular patient the concentration of this drug in the bloodstream immediately after injection is 0.98 µg/mL. What will the concentration be 165 minutes later? Round your answer to 2 significant digits. mL 3 ? x10 X
The rate at which a certain drug is eliminated by the body follows first-order kinetics, with a half life of 33 minutes. Suppose in a particular patient the concentration of this drug in the bloodstream immediately after injection is 0.98 µg/mL. What will the concentration be 165 minutes later? Round your answer to 2 significant digits. mL 3 ? x10 X
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![**Drug Elimination Kinetics Educational Exercise**
Title: First-Order Kinetics in Drug Elimination
---
**Topic:** Understanding First-Order Kinetics in Drug Elimination from the Body
**Objective:** Learn how to calculate the concentration of a drug in the bloodstream over time using first-order kinetics and the concept of half-life.
### Problem Statement:
The rate at which a certain drug is eliminated by the body follows first-order kinetics, with a half-life of 33 minutes.
**Scenario:**
Suppose in a particular patient the concentration of this drug in the bloodstream immediately after injection is 0.98 μg/mL. What will the concentration be 165 minutes later?
**Instructions:**
- Round your answer to 2 significant digits.
**Data Given:**
- Initial concentration (C₀): 0.98 μg/mL
- Half-life (t₁/₂): 33 minutes
- Time elapsed (t): 165 minutes
**Objective:**
Calculate the concentration (C) of the drug in the bloodstream after 165 minutes.
### Solution Steps:
**Using the first-order kinetics formula:**
\[ C = C₀ \times \left( \frac{1}{2} \right)^{\frac{t}{t₁/₂}} \]
Where:
- \( C \) is the concentration after time \( t \).
- \( C₀ \) is the initial concentration.
- \( t \) is the time elapsed.
- \( t₁/₂ \) is the half-life.
Plug in the values:
\[ C = 0.98 \, \text{μg/mL} \times \left( \frac{1}{2} \right)^{\frac{165}{33}} \]
\[ \frac{165}{33} = 5 \]
\[ C = 0.98 \, \text{μg/mL} \times \left( \frac{1}{2} \right)^5 \]
\[ \left( \frac{1}{2} \right)^5 = \frac{1}{32} \]
\[ C = 0.98 \, \text{μg/mL} \times \frac{1}{32} \]
\[ C = 0.030625 \, \text{μg/mL} \]
**Rounded to 2 significant digits:**
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Transcribed Image Text:**Drug Elimination Kinetics Educational Exercise**
Title: First-Order Kinetics in Drug Elimination
---
**Topic:** Understanding First-Order Kinetics in Drug Elimination from the Body
**Objective:** Learn how to calculate the concentration of a drug in the bloodstream over time using first-order kinetics and the concept of half-life.
### Problem Statement:
The rate at which a certain drug is eliminated by the body follows first-order kinetics, with a half-life of 33 minutes.
**Scenario:**
Suppose in a particular patient the concentration of this drug in the bloodstream immediately after injection is 0.98 μg/mL. What will the concentration be 165 minutes later?
**Instructions:**
- Round your answer to 2 significant digits.
**Data Given:**
- Initial concentration (C₀): 0.98 μg/mL
- Half-life (t₁/₂): 33 minutes
- Time elapsed (t): 165 minutes
**Objective:**
Calculate the concentration (C) of the drug in the bloodstream after 165 minutes.
### Solution Steps:
**Using the first-order kinetics formula:**
\[ C = C₀ \times \left( \frac{1}{2} \right)^{\frac{t}{t₁/₂}} \]
Where:
- \( C \) is the concentration after time \( t \).
- \( C₀ \) is the initial concentration.
- \( t \) is the time elapsed.
- \( t₁/₂ \) is the half-life.
Plug in the values:
\[ C = 0.98 \, \text{μg/mL} \times \left( \frac{1}{2} \right)^{\frac{165}{33}} \]
\[ \frac{165}{33} = 5 \]
\[ C = 0.98 \, \text{μg/mL} \times \left( \frac{1}{2} \right)^5 \]
\[ \left( \frac{1}{2} \right)^5 = \frac{1}{32} \]
\[ C = 0.98 \, \text{μg/mL} \times \frac{1}{32} \]
\[ C = 0.030625 \, \text{μg/mL} \]
**Rounded to 2 significant digits:**
\[
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