Question

Three elements X, Y, Z form a Dobereiner triad. The difference in atomic weights between elements Y, Z is 45. If the atomic weight of X is $35$, find the atomic weights of element X, Y, Z?

Answer 1

Hint: If three elements form a Dobereiner ‘s triad then the atomic masses of the middle element is the mean of the atomic masses of first and third elements. The physical and chemical properties are also the same. We will apply this concept according to the given question and get the correct answer.

Complete Step by step answer:
We have been given the difference the atomic weights between the elements Y, Z to be $45$. The atomic weight of element X is given $35$. We know that if three elements form a dobereiner triad then the atomic mass of the middle element is the mean of the atomic mass of a first and third element, then applying the given equation we get
$Z - Y = 45$
Where Z and Y are atomic masses of element Z and Y respectively
Also $Y = \dfrac{{X + Z}}{2}$
$2Y - Z = 35$
Where Y, Z, X are atomic masses of elements Y, X, Z respectively
Solving these two equations we get $X = 35,Y = 80,Z = 125$
Therefore the atomic masses of X, Y, Z respectively are $35,80,125$ respectively.

Hence $X = 35$, $Y = 80$, $Z = 125$.

Additional information: The law of triad holds for three alkali metals namely lithium, sodium and potassium and four other triplets of elements. This model was not a success since the new elements discovered didn’t obey the rule of law of triads and only five of them were identified.

Note: We should cross-check for the correctness of the atomic mass of the given elements by checking whether they are satisfying the theorem of dobereiner triad or not. This means that the atomic mass of Y should be the arithmetic mean of the atomic mass of X and Z. Also the law of triads was an attempt to classify and arrange elements based on the physical and chemical properties.