3g of an oxide of a metal is converted into chloride and it yielded 5g of chloride. Find the equivalent weight of the metal

The correct option is 33.25.

Let the equivalent weight of the metal be represented by $E$.
According to the law of equivalent weights, when a metal oxide is converted into metal chloride, the metal remains the same, and the substances react in the ratio of their equivalent weights.
The equivalent weight of an oxide ion ($O^{2-}$) is 8 g/eq, and the equivalent weight of a chloride ion (${\mathrm{Cl}}^{-}$) is 35.5 g/eq.

Therefore, the equivalent weight of the metal oxide is:
$E_{\text{metal oxide}}=E+8$
And the equivalent weight of the metal chloride is:
$E_{\text{metal chloride}}=E+35.5$

By the law of chemical equivalence, the ratio of the mass of the metal oxide to the mass of the metal chloride is equal to the ratio of their equivalent weights:
$\frac{\text{Mass of metal oxide}}{\text{Mass of metal chloride}}=\frac{E_{\text{metal oxide}}}{E_{\text{metal chloride}}}$

Substituting the given values into the equation:
$\frac{3}{5}=\frac{E+8}{E+35.5}$

Now, we solve for $E$ by cross-multiplying:
$3(E+35.5)=5(E+8)$
$3E+106.5=5E+40$

Rearranging the terms to isolate $E$:
$5E-3E=106.5-40$
$2E=66.5$
$E=\frac{66.5}{2}$
$E=33.25$

Thus, the equivalent weight of the metal is 33.25.