Equivalent weight of a divalent metal is 24. The volume of hydrogen liberated at STP by 12 g of same metal when added to excess of an acid solution is

Options

A. 2.8 litres
B. 5.6 litres
C. 11.2 litres
D. 22.4 litres

Explanation

To solve the problem, we need to find the volume of hydrogen gas liberated at STP when 12 g of a divalent metal is reacted with an excess of acid. Let's break down the solution step by step.

### Step 1: Understanding Equivalent Weight
The equivalent weight of a divalent metal is given as 24 g. The formula for equivalent weight is:

\[ \text{Equivalent Weight} = \frac{\text{Molecular Weight}}{\text{Valency}} \]

Since the metal is divalent, its valency is 2.

### Step 2: Finding Molecular Weight
Using the equivalent weight and valency, we can find the molecular weight of the metal:

\[ \text{Molecular Weight} = \text{Equivalent Weight} \times \text{Valency} = 24 \, \text{g} \times 2 = 48 \, \text{g} \]

### Step 3: Calculating Moles of Metal
Next, we calculate the number of moles of the metal present in 12 g:

\[ \text{Moles of Metal} = \frac{\text{Weight}}{\text{Molecular Weight}} = \frac{12 \, \text{g}}{48 \, \text{g/mol}} = 0.25 \, \text{mol} \]

### Step 4: Writing the Reaction
When the metal reacts with hydrochloric acid (HCl), the reaction can be represented as:

\[ \text{Metal (M)} + 2 \, \text{HCl} \rightarrow \text{Metal Chloride (MCl}_2\text{)} + \text{H}_2 \]

### Step 5: Stoichiometry of the Reaction
From the balanced equation, we see that 1 mole of metal produces 1 mole of hydrogen gas (H₂). Therefore, if we have 0.25 moles of the metal, the amount of hydrogen produced will also be:

\[ \text{Moles of H}_2 = 0.25 \, \text{mol} \]

### Step 6: Calculating Volume of Hydrogen at STP
At standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 liters. Therefore, the volume of hydrogen produced can be calculated as follows:

\[ \text{Volume of H}_2 = \text{Moles of H}_2 \times 22.4 \, \text{L/mol} = 0.25 \, \text{mol} \times 22.4 \, \text{L/mol} = 5.6 \, \text{L} \]

### Final Answer
The volume of hydrogen liberated at STP by 12 g of the metal is **5.6 liters**.

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