**The Problem**

In this problem, we are given the amount of metal carbonate (0.84 gm) and the concentration of sulphuric acid (0.5N). We need to find the equivalent weight of the metal.

**Understanding Equivalent Weight**

Equivalent weight is the weight of a substance that combines or reacts with or displaces one mole of hydrogen ions (H+) or hydroxide ions (OH-) in a chemical reaction. It is a measure of the reactivity of a substance in a given reaction.

**Calculating the Equivalent Weight**

To calculate the equivalent weight of the metal, we can follow these steps:

1. Calculate the number of moles of sulphuric acid:
- Given concentration = 0.5N
- Volume of acid = 40 ml = 0.04 L
- Number of moles of acid = concentration * volume = 0.5 * 0.04 = 0.02 moles

2. Determine the reaction stoichiometry:
- The balanced chemical equation between metal carbonate (MC) and sulphuric acid (H2SO4) is:
MC + H2SO4 → MSO4 + CO2 + H2O
- From the equation, we can see that 1 mole of metal carbonate reacts with 1 mole of sulphuric acid.

3. Calculate the number of moles of metal carbonate:
- From the stoichiometry, we know that the number of moles of metal carbonate is also equal to 0.02 moles.

4. Calculate the molar mass of metal carbonate:
- The molar mass of metal carbonate (MC) can be determined using the given mass of 0.84 gm and the number of moles calculated in step 3.
- Molar mass = mass / moles = 0.84 gm / 0.02 moles = 42 gm/mol

5. Calculate the equivalent weight of metal carbonate:
- The equivalent weight of metal carbonate is equal to its molar mass divided by the number of moles of hydrogen ions (H+) or hydroxide ions (OH-) it reacts with.
- In this case, since the reaction involves sulphuric acid (H2SO4), the metal carbonate reacts with 2 moles of hydrogen ions (H+).
- Therefore, the equivalent weight of metal carbonate = molar mass / 2 = 42 gm/mol / 2 = 21 gm/mol

**Conclusion**

The equivalent weight of the metal in this reaction is 21 gm/mol. This means that 21 grams of the metal carbonate will react with or displace one mole of hydrogen ions in a chemical reaction.

Weight of metal carbonate/GEW = NaXVa in lt  0.84/GEW = 0.5X40/1000  GEW of metal carbonate = 42  GEW of Metal = 42 - GEW of CO3-2 = 42-30 = 12g