6.90 gm of a metal carbonate were dissolved in 60 ml of 2(N) HCl. The excess acid was neutralized by 20 ml of 1(N) NaOH. What is the equivalent wt. of metal ?

Options

A. 40
B. 20
C. 19
D. 39

Explanation

To solve the problem step by step, we need to determine the equivalent weight of the metal in the metal carbonate. Here’s how we can do that:

### Step 1: Calculate the initial equivalents of HCl
We have 60 ml of 2 N HCl. To find the equivalents, we can use the formula:

\[ \text{Equivalents of HCl} = \text{Normality} \times \text{Volume (in liters)} \]

First, convert the volume from ml to liters:

\[ 60 \, \text{ml} = \frac{60}{1000} = 0.060 \, \text{liters} \]

Now calculate the equivalents:

\[ \text{Equivalents of HCl} = 2 \, \text{N} \times 0.060 \, \text{L} = 0.120 \, \text{equivalents} \]

### Step 2: Calculate the equivalents of NaOH used
We have 20 ml of 1 N NaOH. Similarly, we calculate the equivalents:

Convert the volume from ml to liters:

\[ 20 \, \text{ml} = \frac{20}{1000} = 0.020 \, \text{liters} \]

Now calculate the equivalents:

\[ \text{Equivalents of NaOH} = 1 \, \text{N} \times 0.020 \, \text{L} = 0.020 \, \text{equivalents} \]

### Step 3: Calculate the equivalents of HCl that reacted with NaOH
Since NaOH neutralizes the excess HCl, the equivalents of HCl that reacted with NaOH are equal to the equivalents of NaOH:

\[ \text{Equivalents of HCl neutralized} = 0.020 \, \text{equivalents} \]

### Step 4: Calculate the equivalents of HCl that reacted with the metal carbonate
Now, we find the equivalents of HCl that reacted with the metal carbonate:

\[ \text{Equivalents of HCl consumed by metal carbonate} = \text{Initial equivalents of HCl} - \text{Equivalents of HCl neutralized} \]

\[ \text{Equivalents of HCl consumed} = 0.120 - 0.020 = 0.100 \, \text{equivalents} \]

### Step 5: Relate the equivalents of HCl to the metal carbonate
The equivalents of HCl consumed are equal to the equivalents of the metal carbonate:

\[ \text{Equivalents of metal carbonate} = 0.100 \, \text{equivalents} \]

### Step 6: Calculate the equivalent weight of the metal carbonate
We have 6.90 gm of the metal carbonate. The equivalent weight of the metal carbonate can be calculated using:

\[ \text{Equivalent weight of metal carbonate} = \frac{\text{Mass of metal carbonate}}{\text{Equivalents of metal carbonate}} \]

\[ \text{Equivalent weight of metal carbonate} = \frac{6.90 \, \text{g}}{0.100} = 69.0 \, \text{g/equiv} \]

### Step 7: Calculate the equivalent weight of the metal
The metal carbonate can be represented as MCO₃, where M is the metal. The equivalent weight of the carbonate ion (CO₃²⁻) is:

\[ \text{Molar mass of CO₃} = 12 + (16 \times 3) = 60 \, \text{g/mol} \]

The valency of the carbonate ion is 2. Therefore, the equivalent weight of the carbonate is:

\[ \text{Equivalent weight of CO₃} = \frac{60}{2} = 30 \, \text{g/equiv} \]

Now, the equivalent weight of the metal (M) can be calculated as follows:

\[ \text{Equivalent weight of metal carbonate} = \text{Equivalent weight of metal} + \text{Equivalent weight of CO₃} \]

\[ 69.0 = \text{Equivalent weight of metal} + 30 \]

Solving for the equivalent weight of the metal:

\[ \text{Equivalent weight of metal} = 69.0 - 30 = 39.0 \, \text{g/equiv} \]

### Final Answer
The equivalent weight of the metal is **39 g/equiv**.

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