1.12 litre dry chlorine gas at STP was passed over a heated metal when 5.56 g of chloride of the metal was formed. What is the equivalent weight of the metal ?

Answer

To find the equivalent weight of the metal from the given problem, we can follow these steps:

### Step 1: Calculate the number of moles of chlorine gas (Cl2)
At STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 liters. We are given 1.12 liters of Cl2 gas.

\[ \text{Number of moles of } Cl_2 = \frac{\text{Volume of } Cl_2}{\text{Molar volume at STP}} = \frac{1.12 \, \text{L}}{22.4 \, \text{L/mol}} = 0.05 \, \text{moles} \]

### Step 2: Calculate the mass of chlorine in the gas
The molar mass of Cl2 (chlorine gas) is 71 g/mol (since Cl has a molar mass of approximately 35.5 g/mol, and Cl2 has two Cl atoms).

\[ \text{Mass of } Cl_2 = \text{Number of moles} \times \text{Molar mass} = 0.05 \, \text{moles} \times 71 \, \text{g/mol} = 3.55 \, \text{g} \]

### Step 3: Determine the mass of the metal
We know the total mass of the metal chloride formed is 5.56 g. The mass of the chloride (Cl) is 3.55 g, so we can find the mass of the metal (M).

\[ \text{Mass of metal} = \text{Total mass of metal chloride} - \text{Mass of chloride} = 5.56 \, \text{g} - 3.55 \, \text{g} = 2.01 \, \text{g} \]

### Step 4: Calculate the equivalent weight of the metal
To find the equivalent weight of the metal, we need to know how many moles of chloride ions (Cl-) are produced. Since 1 mole of Cl2 produces 2 moles of Cl-, 0.05 moles of Cl2 will produce:

\[ \text{Moles of Cl-} = 0.05 \times 2 = 0.10 \, \text{moles} \]

The equivalent weight of the metal can be calculated using the formula:

\[ \text{Equivalent weight} = \frac{\text{Mass of metal}}{\text{Number of moles of Cl-}} \]

Substituting the values:

\[ \text{Equivalent weight of metal} = \frac{2.01 \, \text{g}}{0.10 \, \text{moles}} = 20.1 \, \text{g/equiv} \]

### Final Answer
The equivalent weight of the metal is **20.1 g/equiv**.

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