In acting as a reduding agent, a piece of metal M weighing 16 grams gives up `2.25 xx 10^(23)` electrons, what is the equivalent weight of the metal

Options

A. 42.83
B. 21.33
C. 83.32
D. 32

Explanation

To find the equivalent weight of the metal M that weighs 16 grams and gives up \(2.25 \times 10^{23}\) electrons, we can follow these steps:

### Step 1: Calculate the number of moles of electrons given up
Using Avogadro's number, which is \(6.022 \times 10^{23}\) electrons/mole, we can find the number of moles of electrons:

\[ \text{Number of moles of electrons} = \frac{\text{Number of electrons}}{\text{Avogadro's number}} = \frac{2.25 \times 10^{23}}{6.022 \times 10^{23}} \]

### Step 2: Calculate the moles of electrons
Now, performing the calculation:

\[ \text{Number of moles of electrons} = \frac{2.25}{6.022} \approx 0.3746 \text{ moles} \]

### Step 3: Determine the equivalent weight of the metal
The equivalent weight of a substance can be calculated using the formula:

\[ \text{Equivalent weight} = \frac{\text{mass of the metal}}{\text{moles of electrons}} \]

Substituting the values we have:

\[ \text{Equivalent weight} = \frac{16 \text{ g}}{0.3746 \text{ moles}} \approx 42.7 \text{ g/equiv} \]

### Step 4: Final Result
Thus, the equivalent weight of the metal M is approximately \(42.7 \text{ g/equiv}\).