Practice Geometric Dilution Problems With Complete Solutions

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Geometric dilution problems are common in various fields such as chemistry, pharmacology, and engineering. They involve the process of reducing concentration or quantity in a systematic geometric progression. Practicing these problems enhances understanding and problem-solving skills. Below, we present several practice problems with complete solutions to help you master geometric dilution calculations.

What is Geometric Dilution?

Geometric dilution involves diluting a solution repeatedly, where each step involves mixing a fixed ratio of the original solution with a diluent. The concentration decreases geometrically, following a specific ratio at each step. The key concept is understanding how the concentration changes after multiple dilutions.

Basic Formula

The concentration after n dilutions can be calculated using the formula:

Cn = C0 × rn

Where:

  • Cn = concentration after n dilutions
  • C0 = initial concentration
  • r = dilution ratio (e.g., 1/2, 1/3, etc.)
  • n = number of dilutions

Practice Problems with Solutions

Problem 1

An initial solution has a concentration of 100 mg/mL. It is diluted by taking 1 mL of the solution and adding it to 4 mL of diluent, and this process is repeated three times. What is the concentration after three dilutions?

Solution:

Each dilution involves a ratio of 1 part solution to 4 parts diluent, so r = 1/5 = 0.2.

Using the formula:

C3 = 100 × (0.2)3 = 100 × 0.008 = 0.8 mg/mL

Problem 2

A solution with an initial concentration of 50 mg/mL is diluted by a factor of 1/10 at each step. What is the concentration after 4 dilutions?

Solution:

Here, r = 1/10 = 0.1, n = 4.

Applying the formula:

C4 = 50 × (0.1)4 = 50 × 0.0001 = 0.005 mg/mL

Additional Practice Problems

  • Calculate the concentration after 5 dilutions if the initial concentration is 200 mg/mL and the dilution ratio is 1/2 at each step.
  • If a solution of 150 mg/mL is diluted by a factor of 1/3 three times, what is the final concentration?
  • Determine the concentration after 6 dilutions starting from 500 mg/mL with a dilution ratio of 1/4 each time.

Practicing these problems regularly will improve your ability to handle geometric dilution calculations efficiently and accurately. Remember to identify the dilution ratio and the number of steps to apply the formula correctly.