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

Answer

To calculate the milli-equivalent of washing soda (sodium carbonate, Na2CO3) required to remove the hardness from 1 liter of hard water containing 18.00 mg of Mg²⁺ ions, we can follow these steps:

### Step 1: Identify the given data
- Mass of Mg²⁺ = 18.00 mg
- Molar mass of magnesium (Mg) = 24 g/mol
- Valence of Mg²⁺ = 2

### Step 2: Calculate the equivalent mass of magnesium
The equivalent mass of an ion can be calculated using the formula:

\[ \text{Equivalent mass} = \frac{\text{Molar mass}}{\text{Valence}} \]

For magnesium:

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

### Step 3: Convert mass of Mg²⁺ to grams
Since the mass of Mg²⁺ is given in milligrams, we need to convert it to grams:

\[ 18.00 \, \text{mg} = 0.018 \, \text{g} \]

### Step 4: Calculate the number of equivalents of Mg²⁺
Using the equivalent mass calculated in Step 2, we can find the number of equivalents of Mg²⁺:

\[ \text{Number of equivalents of Mg}^{2+} = \frac{\text{mass of Mg}^{2+}}{\text{Equivalent mass of Mg}} = \frac{0.018 \, \text{g}}{12 \, \text{g/equiv}} = 0.0015 \, \text{equiv} \]

### Step 5: Convert equivalents to milli-equivalents
Since 1 equivalent = 1000 milli-equivalents, we convert the number of equivalents to milli-equivalents:

\[ 0.0015 \, \text{equiv} = 0.0015 \times 1000 \, \text{milli-equiv} = 1.5 \, \text{milli-equiv} \]

### Step 6: Relate the equivalents of Mg²⁺ to washing soda
The number of milli-equivalents of washing soda required to remove the hardness caused by Mg²⁺ is equal to the number of milli-equivalents of Mg²⁺:

\[ \text{Number of milli-equivalents of Na}_2\text{CO}_3 = 1.5 \, \text{milli-equivalents} \]

### 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 milli-equivalents**.

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