Table of Contents
Welcome to our practice problems section focused on trituration calculations. These challenges are designed to strengthen your understanding of this important process in pharmaceutical compounding. Each problem comes with a detailed solution to guide your learning.
What is Trituration?
Trituration is a process used in pharmacy to reduce the particle size of a solid substance by grinding it into a fine powder. This technique ensures uniform mixing and accurate dosing in compounded medications.
Practice Problem 1: Basic Trituration Calculation
Problem: A pharmacist needs to triturate 50 grams of a medication to a fine powder. If the process reduces the particle size by 25% every 10 minutes, how long will it take to reach a particle size that is 10% of the original?
Solution:
Initial particle size: 100%
Target particle size: 10%
Reduction per 10 minutes: 25%
Number of reductions needed:
- After 1 reduction: 75%
- After 2 reductions: 56.25%
- After 3 reductions: 42.19%
- After 4 reductions: 31.64%
- After 5 reductions: 23.73%
- After 6 reductions: 17.80%
- After 7 reductions: 13.35%
- After 8 reductions: 10.01%
It takes 8 reductions to reach approximately 10% particle size. Since each reduction takes 10 minutes, total time:
8 × 10 minutes = 80 minutes.
Practice Problem 2: Trituration for a Small Quantity
Problem: To prepare a 10-gram sample, a technician triturates the substance for 15 minutes. If the initial particle size is 100%, what is the approximate particle size after this period, assuming a 20% reduction every 5 minutes?
Solution:
Number of reductions:
- Each reduction: 20%
- Time per reduction: 5 minutes
- Total time: 15 minutes
- Number of reductions: 3 (since 15 / 5 = 3)
Particle size after each reduction:
- After 1 reduction: 80%
- After 2 reductions: 64%
- After 3 reductions: 51.2%
Approximate particle size after 15 minutes: 51.2% of the original.
Practice Problem 3: Extended Trituration
Problem: An initial batch of 200 grams of a substance needs to be triturated until the particle size is less than 5%. If the reduction rate is 10% every 15 minutes, how long will the process take?
Solution:
Initial size: 100%
Target size: < 5%
Reduction per 15 minutes: 10%
Number of reductions needed:
- After 1 reduction: 90%
- After 2 reductions: 81%
- After 3 reductions: 72.9%
- After 4 reductions: 65.61%
- After 5 reductions: 59.05%
- After 6 reductions: 53.14%
- After 7 reductions: 47.83%
- After 8 reductions: 43.05%
- After 9 reductions: 38.74%
- After 10 reductions: 34.87%
- After 11 reductions: 31.38%
- After 12 reductions: 28.24%
- After 13 reductions: 25.42%
- After 14 reductions: 22.88%
- After 15 reductions: 20.59%
- After 16 reductions: 18.53%
- After 17 reductions: 16.68%
- After 18 reductions: 15.01%
- After 19 reductions: 13.51%
- After 20 reductions: 12.16%
- After 21 reductions: 10.94%
- After 22 reductions: 9.85%
It takes 22 reductions to reach below 5%. Total time:
22 × 15 minutes = 330 minutes, or 5 hours and 30 minutes.
Summary of Trituration Calculations
Understanding the rate of particle size reduction helps pharmacists plan and execute trituration efficiently. Remember to adjust your calculations based on the specific reduction rate and desired particle size for each compounding task.