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The image contains a material balance problem around a crystallizer unit. There are three output streams: \( A \), \( M \), and \( C \), with compositions for magnesium sulfate (MgSO₄), sodium sulfate (Na₂SO₄), and water (H₂O).

Given:

1. **Feed stream (F)**:  
   Total mass = 100 kg  
   Composition:
   - 0.1 Na₂SO₄
   - 0.2 MgSO₄
   - 0.7 H₂O
   
2. **Stream A** (solid stream):  
   Composition: 1.0 MgSO₄  
   Mass = \( A \, \text{kg} \)

3. **Stream M** (liquid stream):  
   Composition:
   - 0.65 H₂O
   - 0.08 Na₂SO₄
   - The rest is MgSO₄  
   Mass = \( M \, \text{kg} \)

4. **Stream C**:  
   Composition:
   - 0.4621 Na₂SO₄
   - 0.3915 MgSO₄
   - 0.1464 H₂O  
   Mass = \( C \, \text{kg} \)

---

### Balances to Solve:

#### 1. **Sodium Sulfate (Na₂SO₄) Balance:**
Input of Na₂SO₄ from the feed (F):
\[
\text{Na}_2\text{SO}_4 \text{ in } F = 100 \, \text{kg} \times 0.1 = 10 \, \text{kg}
\]

Output of Na₂SO₄ in streams M and C:
\[
\text{Na}_2\text{SO}_4 \text{ in } M = 0.08M
\]
\[
\text{Na}_2\text{SO}_4 \text{ in } C = 0.4621C
\]
So, the balance for Na₂SO₄ is:
\[
10 = 0.08M + 0.4621C
\]

#### 2. **Water (H₂O) Balance:**
Input of water from the feed (F):
\[
\text{H}_2\text{O} \text{ in } F = 100 \, \text{kg} \times 0.7 = 70 \, \text{kg}
\]

Output of water in streams M and C:
\[
\text{H}_2\text{O} \text{ in } M = 0.65M
\]
\[
\text{H}_2\text{O} \text{ in } C = 0.1464C
\]
So, the water balance is:
\[
70 = 0.65M + 0.1464C
\]

#### 3. **Overall Mass Balance (OMB):**
The total mass input is equal to the total mass output:
\[
100 = A + M + C
\]

We are given the final results as \( A = 10.1079 \, \text{kg} \), \( M = 106.9899 \, \text{kg} \), and \( C = 3.1180 \, \text{kg} \). 

---

Would you like a detailed solution for how these balances are solved step-by-step? 

### 5 Related Questions:
1. How can the mass balance for MgSO₄ be formulated in this system?
2. What assumptions are being made in this crystallizer process?
3. How is the crystallization efficiency determined?
4. What would happen if the composition of the feed stream changes?
5. How can you perform an energy balance alongside this material balance?

### Tip:
When performing material balances, always start with the component balances for substances present in only a few streams, as they can simplify the problem significantly.

Perform a material balance around a crystallizer unit with given feed and output stream compositions to solve for the unknown masses in streams A, M, and C.

Learn how to solve a material balance problem involving a crystallizer unit. The feed stream has specific compositions of Na₂SO₄, MgSO₄, and water. Solve for unknown masses in output streams using component balances for Na₂SO₄ and H₂O along with the overall mass balance. Final results are A = 10.1079 kg, M = 106.9899 kg, C = 3.1180 kg.

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