How much water must be evaporated from 90ml of a 50% salt solution to increase its concentration to 75%?.

To find how much water must be evaporated from 90 ml of a 50% salt solution to increase its concentration to 75%, we can use the concept of mass balance, which involves the following steps:

### Step 1: Define the Variables
- Let \( x \) be the amount of water to be evaporated.
- Initially, we have 90 ml of solution, with 50% salt. Therefore, the amount of salt in the solution is:
  \[
  \text{Salt amount} = 90 \, \text{ml} \times 0.50 = 45 \, \text{ml of salt}
  \]

### Step 2: Final Concentration
- After evaporating \( x \) ml of water, the new volume of the solution will be \( 90 - x \) ml.
- We want the final concentration to be 75%, so the amount of salt in the solution should still be 45 ml (since evaporation only removes water, not salt).

### Step 3: Set Up the Equation
The new concentration of the solution should be 75%. Therefore, the amount of salt (45 ml) should make up 75% of the new volume \( (90 - x) \) ml:
\[
\frac{45}{90 - x} = 0.75
\]

### Step 4: Solve for \( x \)
Now, solve the equation:
\[
45 = 0.75 \times (90 - x)
\]
\[
45 = 67.5 - 0.75x
\]
\[
0.75x = 67.5 - 45 = 22.5
\]
\[
x = \frac{22.5}{0.75} = 30 \, \text{ml}
\]

### Conclusion
You must evaporate **30 ml** of water to increase the concentration of the salt solution to 75%.

Would you like further clarification, or should I go into more detail on any part of the process?

Here are five related questions:
1. How would the solution change if the initial concentration was 30% instead of 50%?
2. What if we needed to reach a concentration of 90% salt instead of 75%?
3. Can this method be applied to other substances, like sugar solutions?
4. How would the evaporation process affect the temperature of the solution?
5. What is the mathematical model used to describe the concentration of salt in terms of water evaporated?

Tip: Always ensure the amount of the substance (like salt) remains constant when evaporation is involved, as evaporation only affects the solvent (water).

How much water must be evaporated from 90ml of a 50% salt solution to increase its concentration to 75%?

Find out how to calculate the amount of water that must be evaporated from 90ml of a 50% salt solution to achieve a 75% concentration. This problem involves mass balance and algebraic concepts suitable for Grades 9-11.

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