Question

When a Dobereiner's triad is considered, the sum of atomic weights of the terminal elements $X$ and $Z$ is 162.5. The atomic weight of $Z$ is 50 units less than 5 times that of $X$. Identify the periods of $X,Y$ and $Z$ respectively in the present periodic table.

• A. $3,4,5$
• B. $4,5,6$
• C. $2,3,4$
• D. $3,5,4$

Answer 1

Answer: (A)

$3,4,5$

Let the atomic weights (in g/mol) of elements X, Y and Z be x, y and z respectively.
The atomic weight of Z is 50 units less than 5 times that of X.

$z=5x-50$.....(1)

The sum of atomic weights of the terminal elements X and Z is 162.5
$x+z=162.5$
$z=162.5-x$......(2)

Substitute (2) into (1)
$162.5-x=5x-50$
$162.5=6x-50$
$6x=212.5$
$x=35.4$

Substitute this in equation (2)
$z=162.5-x=162.5-35.4=127.1$

The atomic weight of Y is the arithmetic mean of the atomic weights of X and Z.
$y=\frac{x+z}{2}$
$y=\frac{35.4+127.1}{2}=81.3$

From the periodic table, we see that the elements with atomic weights 35.4, 81.3 and 127.1 belong to 3 (chlorine), 4 (bromine) and 5 (iodine).

Hence, the option (A) is the correct answer.