If a liter of chemical X is 95% pure, how many liters of water must be added to make a 50% solution?

To solve this problem, we need to dilute the chemical solution from 95% purity to 50% purity by adding water. Here's how to approach it:

### Step-by-step solution:

1. **Initial Amount of Pure Chemical X**:
   - You have 1 liter of chemical X, which is 95% pure.
   - This means the amount of pure chemical X in the solution is:
   \[
   \text{Amount of pure chemical} = 1 \times 0.95 = 0.95 \text{ liters}
   \]
   
2. **Final Solution**:
   - After adding water, the final solution should be 50% pure, meaning 50% of the total volume will be pure chemical X.
   - Let \( V \) be the final total volume (in liters) of the solution after adding water.
   - Since the amount of pure chemical X remains constant at 0.95 liters, the final solution must satisfy:
   \[
   \frac{0.95}{V} = 0.50
   \]
   
3. **Solve for \( V \)**:
   \[
   V = \frac{0.95}{0.50} = 1.9 \text{ liters}
   \]

4. **Amount of Water to Add**:
   - The total volume of the solution after adding water will be 1.9 liters.
   - Since you started with 1 liter of chemical X solution, the amount of water to add is:
   \[
   \text{Water to add} = 1.9 - 1 = 0.9 \text{ liters}
   \]

### Final Answer:
You need to add **0.9 liters of water** to dilute the chemical X to a 50% solution.

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Do you need further details or have any questions? Here are some related questions to expand on the topic:

1. How would the process change if the starting solution were only 75% pure?
2. What if you wanted to dilute the solution to 25% purity instead of 50%?
3. How would you handle this problem if the volume of the initial solution was different?
4. Could you calculate the concentration if a different amount of water was added?
5. What is the minimum purity achievable if you keep adding water indefinitely?

**Tip**: When diluting solutions, the amount of the solute (pure chemical) remains constant, only the total volume changes!

Learn how to dilute a 95% pure solution of chemical X to 50% purity by adding water. This problem involves key mathematical concepts such as percentage, dilution, and algebra. Step-by-step solution suitable for Grades 9-12 students.

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