A chloride of a metal contains 47.23% of the metal. Find out the equivalent weight of the metal.

Answer

To find the equivalent weight of the metal in the given chloride, we can follow these steps:

### Step 1: Understand the composition of the metal chloride
We are given that the chloride of a metal contains 47.23% of the metal. This means that if we consider 100 grams of the metal chloride, it contains:
- Metal: 47.23 grams
- Chloride: 100 grams - 47.23 grams = 52.77 grams

### Step 2: Identify the equivalent weight of the anion (chloride)
Chloride is derived from chlorine, which has an atomic weight of approximately 35.5 g/mol. Since chloride (Cl-) has a charge of -1, its equivalent weight is the same as its atomic weight:
- Equivalent weight of chloride = 35.5 g

### Step 3: Set up the relationship between the metal and chloride
In a metal chloride, the number of equivalents of the metal will equal the number of equivalents of the chloride. This can be expressed as:
\[ \frac{\text{Weight of Metal}}{\text{Equivalent Weight of Metal}} = \frac{\text{Weight of Chloride}}{\text{Equivalent Weight of Chloride}} \]

### Step 4: Substitute the known values into the equation
We can substitute the values we have:
\[ \frac{47.23 \text{ g}}{E_m} = \frac{52.77 \text{ g}}{35.5 \text{ g}} \]
where \(E_m\) is the equivalent weight of the metal.

### Step 5: Solve for the equivalent weight of the metal
Cross-multiplying gives us:
\[ 47.23 \times 35.5 = 52.77 \times E_m \]
Calculating the left side:
\[ 47.23 \times 35.5 = 1675.565 \]
Now, we can solve for \(E_m\):
\[ E_m = \frac{1675.565}{52.77} \]
Calculating this gives:
\[ E_m \approx 31.71 \text{ g} \]

### Conclusion
The equivalent weight of the metal is approximately **31.71 grams**.

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