4) How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution?

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
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### Mixture Problem: Alcohol Solution

**Objective**: Determine the quantity of 20% alcohol solution to be added to 40 liters of a 50% alcohol solution to achieve a 30% alcohol solution.

**Question 4**:  
- How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution?

**Table Overview**:

A table is provided with three columns:

1. **Solution Strength (%)**:
   - Lists the percentage concentration of alcohol in the solution.
   
2. **Liters**:
   - Contains the quantity in liters for each solution type.

3. **Total Liters of % Acid**:
   - Represents the total volume of alcohol in the solution after blending.

The table is divided into rows, where each row corresponds to a particular solution calculation.

**Work through this problem by setting up an equation**:
- Let \( x \) be the liters of 20% solution. The equation based on alcohol content can be derived from:

\[ 0.2x + 0.5(40) = 0.3(x + 40) \]

### Steps to Solve

1. Calculate the total alcohol in each solution.
2. Use the equation to find the value of \( x \).
3. Fill in the table based on the solution.

This exercise aids in understanding mixture problems and applying percentages in practical scenarios.
Transcribed Image Text:### Mixture Problem: Alcohol Solution **Objective**: Determine the quantity of 20% alcohol solution to be added to 40 liters of a 50% alcohol solution to achieve a 30% alcohol solution. **Question 4**: - How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution? **Table Overview**: A table is provided with three columns: 1. **Solution Strength (%)**: - Lists the percentage concentration of alcohol in the solution. 2. **Liters**: - Contains the quantity in liters for each solution type. 3. **Total Liters of % Acid**: - Represents the total volume of alcohol in the solution after blending. The table is divided into rows, where each row corresponds to a particular solution calculation. **Work through this problem by setting up an equation**: - Let \( x \) be the liters of 20% solution. The equation based on alcohol content can be derived from: \[ 0.2x + 0.5(40) = 0.3(x + 40) \] ### Steps to Solve 1. Calculate the total alcohol in each solution. 2. Use the equation to find the value of \( x \). 3. Fill in the table based on the solution. This exercise aids in understanding mixture problems and applying percentages in practical scenarios.
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