Question

The equivalent weights of an element of variable valency are 21 and 14. The atomic mass of the element may be:
A) 35
B) 42
C) 72
D) 126

Answer 1

Hint: the answer to this question includes the basic concept of chemistry that deals with the calculation of equivalent weight by using its formula that is given by, $Eq.Wt.={\displaystyle \frac{M}{valency}}$

Complete answer:
In the previous chapters of chemistry, we have come across the chapters of inorganic chemistry that deals with the calculation of molecular weight, molar mass and also equivalent mass of the elements.
Now, let us find the equivalent weight of an individual element based on its formula.
Let us first go through the basic definition of equivalent weight which will help us to easily calculate the atomic mass.
- Equivalent weight / mass is the mass of a given substance which combines with or displaces a fixed quantity of another substance.
- Equivalent weight is also defined as the ratio of molecular weight of the compound formula to that of the valence it assumes in compounds.
- Based on all these above facts, the data given is as follows
Let ‘x’ be the valency of the element 1 which has the equivalent weight $E_1=21$
Let ‘y’ be the valency of the element 2 with the equivalent weight $E_2=14$
If we take M as the atomic mass as per the data,
$E_1={\displaystyle \frac{M}{x}}=21$ and $E_2={\displaystyle \frac{M}{y}}=14$
Now, the ratio of these two are${\displaystyle \frac{E_2}{E_1}}={\displaystyle \frac{M/y}{M/x}}={\displaystyle \frac{x}{y}}={\displaystyle \frac{2}{3}}$
This implies that x = 2 and y = 3
Now, $E_1={\displaystyle \frac{M}{x}}={\displaystyle \frac{M}{2}}=21$ and $E_2={\displaystyle \frac{M}{y}}={\displaystyle \frac{M}{3}}=14$
$$\Rightarrow E_1=2\times 21=M$$ and $E_2=3\times 14=M$
Therefore, we get the values of equivalents weights of element 1 and element 2 as M = 42 and M = 42 respectively.

Therefore, the correct answer is option B) 42.

Note: Note that equivalent weight and gram equivalent weight are the same numerical denotations but change it has is in the units for equivalent weight it is atomic mass units and for gram equivalent weight, it is measured in grams.