A chemist has one solution which is 50% acidic and a second which is 25% acidic. How much of each should be mixed to make 10 litre of 40% acid solution

This is a classic mixture problem, where we are asked to mix two solutions of different acid concentrations to obtain a desired concentration. Let’s define the variables:

- Let \( x \) be the amount (in liters) of the 50% acidic solution.
- Let \( 10 - x \) be the amount (in liters) of the 25% acidic solution, since the total volume is 10 liters.

The amount of acid in each solution is:

- From the 50% solution: \( 0.50x \) liters of acid.
- From the 25% solution: \( 0.25(10 - x) \) liters of acid.

The total amount of acid in the mixture should equal 40% of the total 10 liters, i.e., \( 0.40 \times 10 = 4 \) liters.

We now form the equation:
\[
0.50x + 0.25(10 - x) = 4
\]

### Solving the equation:

1. Distribute the \( 0.25 \) on the left-hand side:
   \[
   0.50x + 0.25(10) - 0.25x = 4
   \]
   \[
   0.50x + 2.5 - 0.25x = 4
   \]

2. Combine like terms:
   \[
   (0.50x - 0.25x) + 2.5 = 4
   \]
   \[
   0.25x + 2.5 = 4
   \]

3. Subtract 2.5 from both sides:
   \[
   0.25x = 1.5
   \]

4. Solve for \( x \):
   \[
   x = \frac{1.5}{0.25} = 6
   \]

So, you need **6 liters** of the 50% acidic solution.

Since the total is 10 liters, the amount of the 25% acidic solution is:
\[
10 - 6 = 4 \text{ liters}.
\]

### Conclusion:
- **6 liters** of the 50% acidic solution.
- **4 liters** of the 25% acidic solution.

Would you like more details or have any questions?

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Here are 5 related questions to expand your understanding:

1. How would the amounts change if you needed 20 liters of 40% acidic solution instead of 10 liters?
2. What would happen if the required concentration was 35% instead of 40%?
3. Can you solve the problem using a system of equations?
4. How much of each solution would you need to mix if you had only 5 liters of the 50% solution available?
5. What is the general formula for solving mixture problems like this one?

**Tip:** When solving mixture problems, always define variables carefully and write an equation based on the total amount of the substance being mixed (in this case, acid).

A chemist has one solution which is 50% acidic and a second which is 25% acidic. How much of each should be mixed to make 10 liters of 40% acid solution?

Discover how to solve a classic mixture problem where a chemist mixes 50% and 25% acidic solutions to create 10 liters of a 40% acid solution. Follow the step-by-step process involving algebraic equations and mixture concepts. Ideal for students in Grades 8-10.

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