A concentration process increases the solid content of 250kg of fresh tomato
juice from 13.5% to 59%. Write an expression for the mass balance of the
process and calculate the amount of concentrate produced.


### Step 1: Mass Balance Equation

The mass balance for this concentration process focuses on the solids (dry matter) in the tomato juice, as the water content changes but the solid content remains constant.

Let:
- \( m_{\text{fresh}} \) = mass of fresh tomato juice (250 kg),
- \( X_{\text{initial}} \) = initial solid content (13.5% = 0.135),
- \( X_{\text{final}} \) = final solid content (59% = 0.59),
- \( m_{\text{concentrate}} \) = mass of the concentrate.

The total mass of solids before and after concentration is the same:

\[
m_{\text{fresh}} \times X_{\text{initial}} = m_{\text{concentrate}} \times X_{\text{final}}
\]

### Step 2: Solve for the Mass of Concentrate

Rearranging the equation to solve for \( m_{\text{concentrate}} \):

\[
m_{\text{concentrate}} = \frac{m_{\text{fresh}} \times X_{\text{initial}}}{X_{\text{final}}}
\]

Substitute the values:

\[
m_{\text{concentrate}} = \frac{250 \times 0.135}{0.59}
\]

Now, let's calculate the mass of the concentrate.The mass of the concentrate produced is approximately 57.20 kg.

### Summary:
- The initial mass of tomato juice: 250 kg.
- The mass of concentrate after the process: 57.20 kg.

Would you like further details on the process or any clarifications?

Here are some related questions for further exploration:
1. How much water is removed during the concentration process?
2. What would happen if the final solid content was higher than 59%?
3. How would the process change if the initial solid content were lower?
4. How is the solid content measured in practical applications?
5. What equipment is commonly used for concentration processes in food industries?

**Tip:** When performing mass balance calculations, focus on preserving the total amount of the key component (e.g., solids) across different stages of the process.

A concentration process increases the solid content of 250kg of fresh tomato juice from 13.5% to 59%. Write an expression for the mass balance of the process and calculate the amount of concentrate produced.

Understand the mass balance of a concentration process where the solid content of 250 kg of fresh tomato juice increases from 13.5% to 59%. This step-by-step solution provides key formulas and calculations, resulting in a concentrate mass of 57.20 kg. Ideal for students in Grades 9-12.

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