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# A binary compound of zinc and Sulphur contains $67.1\%$zinc by mass. The ratio of zinc and Sulphur atoms in the compound is $x:y$. Then, $x + y$is: [$Zn = 65$; $S{{ = }}32$]

Last updated date: 20th Jun 2024
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Hint: Since we are given the percentage composition of the metal and Sulphur in the compound, we can say that the total mass will be $100grams$ and hence the mass of zinc will be equal to its percentage composition. To find the ratio of atoms, find the ratio of number of moles in the given species.

In the question, we have been given the value of the mass percentage of zinc as $67.1\%$ by mass.
This means that $67.1gram$ of zinc will be present in $100grams$ of the total compound.
Given Mass of the $Zn$ is $67.1grams$
From this we get mass of $S$ which will be: $Total\,mass - Mass\,of\,zinc$
Substituting the values, we get:
$100 - 67.1 = 32.9grams$
Now calculating the ratio of mass zinc and Sulphur
$Zn:S::67.1:32.9$
As we know that the molecular weight of zinc is $65.3$
And Molecular weight of Sulphur is $32$
Now calculating moles of zinc and Sulphur

$Moles = \dfrac{{Given\,mass}}{{molecular\,mass}}$

Substituting this value, in the ratio formula, we get:

$Zn:S = \dfrac{{\dfrac{{mass\,of\,zinc}}{{molecular\,mass\,of\,zinc}}}}{{\dfrac{{mass\,of\,Sulphur}}{{molecular\, mass\,of\,sulphur}}}}$

Substituting the values, we get:

$Zn:S = \dfrac{{\dfrac{{67.1}}{{65.3}}}}{{\dfrac{{32.9}}{{32}}}}$

Solving this value, we get the ratio as $1:1$

As per question the asked $x + y$ value is

comparing $x:y$ with $1:1$

Hence $x = 1$

$y = 1$

$x + y = 1 + 1 = 2$

Note: Law of constant proportion states that two elements combine in a fixed ratio when they have to form a molecule. Hence whenever Zinc and sulphide combine is the ratio of one is to one, they will form the same molecule everytime.