Solving Concentration Problems: A Step-by-Step Guide

Mixtures and concentration problems are a fundamental part of chemistry and play a significant role in areas such as pharmaceuticals, engineering, and everyday household activities. In this article, we will explore a common problem related to solution concentration, particularly focusing on how to enhance the concentration of alcohol in a given mixture. We'll break down the solution process step-by-step for a better understanding.

Understanding the Initial Mixture

Let's start with an example: suppose we have a 80-liter solution that contains 30 liters of alcohol. This means the solution is composed of 30 liters of alcohol and 50 liters of water. The concentration of alcohol in the initial solution can be calculated as follows:

30 liters of alcohol out of a total 80 liters 30/80 * 100 37.5% alcohol

Objective

The objective is to determine how many liters of pure alcohol need to be added to this existing solution to increase the concentration of alcohol to 65%. To achieve this, we need to set up an equation that reflects this new concentration.

Setting Up the Equation

Let's denote the volume of pure alcohol added as x liters. After adding x liters of pure alcohol to the initial 80 liters, the total volume of the new solution will be (80 x) liters. The amount of alcohol in the new solution will be (30 x) liters.

The concentration equation will be:

(30 x) / (80 x) 65/100

Simplifying this equation:

30 x (65/100) * (80 x)

Let's solve for x.

Solving the Equation

Multiply both sides by (80 x): (30 x) * 100 65 * (80 x) 3000 10 5200 65x Subtract 65x from both sides: 35x 2200 Solve for x: x 2200 / 35 62.86

Therefore, approximately 62.86 liters of pure alcohol must be added to the initial 80-liter solution to achieve a concentration of 65% alcohol.

Conclusion

Understanding how to solve concentration problems can be crucial in various industries and everyday situations. By following the step-by-step process outlined above, you can easily determine the required amount of pure alcohol to add to any given solution to achieve a desired final concentration.

Related Keywords

alcohol concentration, solution chemistry, mixture problems