One litre hard water contains 12.00 mg `Mg^(2+)` millieqivalent of washing soda required to remove its hardness is

Options

A. (a)1
B. (b)12.15
C. (c )`1xx10^(-3)`
D. (d)`12.5xx10^(-3)`

Explanation

To solve the problem of determining the milliequivalent of washing soda required to remove the hardness from 1 litre of hard water containing 12.00 mg of \( Mg^{2+} \), we can follow these steps:

### Step 1: Understand the Concept of Milliequivalents
Milliequivalents (mEq) are a measure of the reactive capacity of a substance. For ions, it is calculated based on the charge of the ion and its molar mass.

### Step 2: Calculate the Milliequivalents of \( Mg^{2+} \)
We need to calculate the milliequivalents of \( Mg^{2+} \) present in the hard water. The formula for milliequivalents is:

\[ \text{Milliequivalents} = \frac{\text{Weight (g)}}{\text{Equivalent Weight (g/equiv)}} \times 1000 \]

### Step 3: Determine the Equivalent Weight of \( Mg^{2+} \)
The equivalent weight of an ion can be calculated using the formula:

\[ \text{Equivalent Weight} = \frac{\text{Molar Mass}}{\text{Valency}} \]

For \( Mg^{2+} \):
- Molar Mass of \( Mg \) = 24 g/mol
- Valency of \( Mg^{2+} \) = 2

Thus, the equivalent weight of \( Mg^{2+} \) is:

\[ \text{Equivalent Weight of } Mg^{2+} = \frac{24 \, \text{g/mol}}{2} = 12 \, \text{g/equiv} \]

### Step 4: Substitute Values into the Milliequivalent Formula
Now, substituting the values into the milliequivalent formula for \( Mg^{2+} \):

\[ \text{Milliequivalents of } Mg^{2+} = \frac{12 \times 10^{-3} \, \text{g}}{12 \, \text{g/equiv}} \times 1000 \]

### Step 5: Calculate the Result
Performing the calculation:

\[ \text{Milliequivalents of } Mg^{2+} = \frac{12 \times 10^{-3}}{12} \times 1000 = 1 \, \text{mEq} \]

### Step 6: Conclusion
Since the milliequivalents of washing soda required to remove the hardness is equal to the milliequivalents of \( Mg^{2+} \), we conclude that:

\[ \text{Milliequivalents of washing soda required} = 1 \, \text{mEq} \]

Thus, the answer is **1 milliequivalent**.

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