0.32 g of metal gave on treatment with an acid 112 mL of hydrogen at NTP. Calculate the equivalent weight of the metal

Options

A. 58
B. 32
C. 11.2
D. 24

Explanation

To calculate the equivalent weight of the metal based on the given data, we can follow these steps:

### Step 1: Convert the volume of hydrogen gas from mL to L
The volume of hydrogen gas given is 112 mL. We need to convert this to liters.

\[ \text{Volume in L} = \frac{112 \text{ mL}}{1000} = 0.112 \text{ L} \]

### Step 2: Calculate the number of moles of hydrogen gas
At Normal Temperature and Pressure (NTP), 1 mole of gas occupies 22.4 L. We can use this to find the number of moles of hydrogen gas produced.

\[ \text{Number of moles of } H_2 = \frac{\text{Volume of } H_2}{22.4 \text{ L}} = \frac{0.112 \text{ L}}{22.4 \text{ L/mol}} \approx 0.005 \text{ moles} \]

### Step 3: Determine the equivalent weight of hydrogen
The equivalent weight of hydrogen (H) is 1 g/mol. Since 1 mole of hydrogen corresponds to 2 g of H2, we can find the mass of hydrogen produced.

\[ \text{Mass of } H_2 = \text{Number of moles} \times \text{Molar mass of } H_2 = 0.005 \text{ moles} \times 2 \text{ g/mol} = 0.01 \text{ g} \]

### Step 4: Relate the mass of the metal to the mass of hydrogen produced
From the stoichiometry of the reaction, the mass of the metal that produced the hydrogen can be related to the equivalent weight of the metal. We know that 0.32 g of metal produced 0.01 g of hydrogen.

### Step 5: Calculate the equivalent weight of the metal
The equivalent weight of the metal can be calculated using the formula:

\[ \text{Equivalent weight of metal} = \frac{\text{mass of metal}}{\text{number of equivalents of H}_2} \]

Since 1 equivalent of H2 corresponds to 1 g of H2, we can calculate:

\[ \text{Number of equivalents of } H_2 = \frac{0.01 \text{ g}}{1 \text{ g/equiv}} = 0.01 \text{ equivalents} \]

Now substituting the values:

\[ \text{Equivalent weight of metal} = \frac{0.32 \text{ g}}{0.01 \text{ equivalents}} = 32 \text{ g/equiv} \]

### Final Answer
The equivalent weight of the metal is **32 g/equiv**.

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