The ionic strength of solution containing 0.5 M `MgSO_(4), 0.1M AlCl_(3)` and `0.2M (NH_(4))_(2)SO_(4)` is

Options

A. 0.75
B. 1.85
C. 3.2
D. 1.5

Answer

To calculate the ionic strength of the solution containing 0.5 M `MgSO4`, 0.1 M `AlCl3`, and 0.2 M `(NH4)2SO4`, we will follow these steps:

### Step 1: Understand the formula for ionic strength
The ionic strength (I) of a solution is given by the formula:
\[ I = \frac{1}{2} \sum (C_i z_i^2) \]
where:
- \( C_i \) = concentration of each ion
- \( z_i \) = charge of each ion

### Step 2: Identify the ions and their concentrations
1. **For Magnesium Sulfate (MgSO4)**:
- It dissociates into `Mg^2+` and `SO4^2-`.
- Concentration of `Mg^2+` = 0.5 M, \( z = +2 \)
- Concentration of `SO4^2-` = 0.5 M, \( z = -2 \)

2. **For Aluminum Chloride (AlCl3)**:
- It dissociates into `Al^3+` and 3 `Cl^-`.
- Concentration of `Al^3+` = 0.1 M, \( z = +3 \)
- Concentration of `Cl^-` = 0.1 M × 3 = 0.3 M, \( z = -1 \)

3. **For Ammonium Sulfate ((NH4)2SO4)**:
- It dissociates into 2 `NH4^+` and `SO4^2-`.
- Concentration of `NH4^+` = 0.2 M × 2 = 0.4 M, \( z = +1 \)
- Concentration of `SO4^2-` = 0.2 M, \( z = -2 \)

### Step 3: Calculate the contributions to ionic strength
Now we will calculate the contributions to ionic strength from each ion:

1. **From MgSO4**:
\[ I_{MgSO4} = C_{Mg^2+} z_{Mg^2+}^2 + C_{SO4^{2-}} z_{SO4^{2-}}^2 \]
\[ = 0.5 \times (2^2) + 0.5 \times (2^2) = 0.5 \times 4 + 0.5 \times 4 = 2 + 2 = 4 \]

2. **From AlCl3**:
\[ I_{AlCl3} = C_{Al^{3+}} z_{Al^{3+}}^2 + C_{Cl^-} z_{Cl^-}^2 \]
\[ = 0.1 \times (3^2) + 0.3 \times (1^2) = 0.1 \times 9 + 0.3 \times 1 = 0.9 + 0.3 = 1.2 \]

3. **From (NH4)2SO4**:
\[ I_{(NH4)2SO4} = C_{NH4^+} z_{NH4^+}^2 + C_{SO4^{2-}} z_{SO4^{2-}}^2 \]
\[ = 0.4 \times (1^2) + 0.2 \times (2^2) = 0.4 \times 1 + 0.2 \times 4 = 0.4 + 0.8 = 1.2 \]

### Step 4: Sum the contributions
Now, we sum the contributions from all the ions:
\[ \text{Total} = I_{MgSO4} + I_{AlCl3} + I_{(NH4)2SO4} = 4 + 1.2 + 1.2 = 6.4 \]

### Step 5: Calculate the ionic strength
Now, we apply the ionic strength formula:
\[ I = \frac{1}{2} \times 6.4 = 3.2 \]

### Final Answer
The ionic strength of the solution is **3.2**.

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