 A pot contains 6 L brine at a concentration of 120 g/L. How much of the water should be boilded off to increase the concentration to 200 g/L?


To solve this problem, let's break it down into steps:

### Step 1: Define the variables
- \( V \) is the initial volume of the brine, which is 6 liters (L).
- \( C_1 \) is the initial concentration of the brine, which is 120 g/L.
- \( C_2 \) is the final concentration of the brine, which is 200 g/L.
- \( V_f \) is the final volume of the brine after boiling off some water.
- \( m \) is the amount of salt, which remains constant since only water is being boiled off.

### Step 2: Calculate the initial amount of salt
The amount of salt in the solution initially is:

\[
m = C_1 \times V = 120 \, \text{g/L} \times 6 \, \text{L} = 720 \, \text{g}
\]

### Step 3: Set up the equation for the final concentration
After boiling off some water, the final concentration \( C_2 \) is given by:

\[
C_2 = \frac{m}{V_f}
\]

Substituting the known values:

\[
200 \, \text{g/L} = \frac{720 \, \text{g}}{V_f}
\]

### Step 4: Solve for \( V_f \)
Rearrange the equation to solve for the final volume \( V_f \):

\[
V_f = \frac{720 \, \text{g}}{200 \, \text{g/L}} = 3.6 \, \text{L}
\]

### Step 5: Calculate the volume of water to be boiled off
The amount of water to be boiled off is the difference between the initial volume and the final volume:

\[
\text{Volume of water to be boiled off} = V - V_f = 6 \, \text{L} - 3.6 \, \text{L} = 2.4 \, \text{L}
\]

### Final Answer
You need to boil off **2.4 liters** of water to increase the concentration of the brine to 200 g/L.

Would you like more details or have any questions? Here are some related questions:

1. What would the concentration be if you boiled off 3 liters of water?
2. How does the concentration change if no water is boiled off?
3. Can this problem be solved using a different approach, such as a proportion method?
4. What if the initial concentration was different, say 150 g/L?
5. How does this concept apply to real-world situations like cooking or chemical processing?

**Tip:** Always double-check the units when performing concentration and volume calculations to ensure consistency.

Learn how to increase the concentration of a brine solution from 120 g/L to 200 g/L by boiling off water. This problem involves calculating the initial and final concentrations, understanding the relationship between volume and concentration, and determining the amount of water to be boiled off. Suitable for high school students.

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