Calculate milli equilvalent of washing soda required to remove its hardness from one litre hard water contains `"18.00 mg Mg"^(2+)`

Answer

To solve the problem of calculating the milli-equivalents of washing soda required to remove the hardness from 1 liter of hard water containing 18.00 mg of Mg²⁺, we can follow these steps:

### Step 1: Understand the Concept of Milli-Equivalent
A milli-equivalent (mEq) is a unit that expresses the amount of a substance in terms of its reactive capacity. For ions, it is calculated based on the number of moles of the ion and its charge.

### Step 2: Calculate the Equivalent Weight of Magnesium
The equivalent weight of an ion can be calculated using the formula:
\[ \text{Equivalent Weight} = \frac{\text{Molar Mass}}{n} \]
where \( n \) is the number of electrons transferred (valency).

For magnesium (Mg):
- Molar Mass = 24 g/mol
- Valency (n) = 2

Thus, the equivalent weight of Mg is:
\[ \text{Equivalent Weight of Mg} = \frac{24 \, \text{g/mol}}{2} = 12 \, \text{g/equiv} \]

### Step 3: Convert the Mass of Magnesium to Grams
We have 18.00 mg of Mg²⁺. We need to convert this to grams:
\[ 18.00 \, \text{mg} = 18.00 \times 10^{-3} \, \text{g} = 0.018 \, \text{g} \]

### Step 4: Calculate the Number of Equivalents of Magnesium
Using the equivalent weight calculated in Step 2, we can find the number of equivalents of Mg²⁺:
\[ \text{Number of Equivalents} = \frac{\text{Mass (g)}}{\text{Equivalent Weight (g/equiv)}} \]
\[ \text{Number of Equivalents of Mg} = \frac{0.018 \, \text{g}}{12 \, \text{g/equiv}} = 0.0015 \, \text{equiv} \]

### Step 5: Convert Equivalents to Milli-Equivalents
Since 1 equivalent = 1000 milli-equivalents, we convert the number of equivalents to milli-equivalents:
\[ \text{Milli-Equivalents of Mg} = 0.0015 \, \text{equiv} \times 1000 = 1.5 \, \text{mEq} \]

### Step 6: Relate to Washing Soda
Washing soda (sodium carbonate, Na₂CO₃) reacts with Mg²⁺ to remove hardness. The amount of washing soda required in milli-equivalents will be equal to the milli-equivalents of Mg²⁺ present in the water.

Thus, the milli-equivalents of washing soda required is also:
\[ \text{Milli-Equivalents of Washing Soda} = 1.5 \, \text{mEq} \]

### Final Answer
The milli-equivalent of washing soda required to remove the hardness from 1 liter of hard water containing 18.00 mg of Mg²⁺ is **1.5 mEq**.

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