Question

A certain sample of cuprous sulphide is found to have the composition \[C{u_{1.95}}{S_{1.00}}\]because of incorporation of \[C{u^{2 + }}\] and \[C{u^ + }\] ions in the crystal then ratio of \[C{u^{2 + }}\]and \[C{u^ + }\]ion is:
A: 0.08 and 1.00
B: 1 : 38
C: 1 : 24
D: 1.00 : 1.00

Answer 1

Hint: Copper Sulphide (\[C{u_2}S\]), consisting of copper and sulphur, naturally occur as mineral chalcocite. It is synthesized on heating copper in the presence of ${H_2}S$.

Complete step by step answer:
In order to calculate the chemical formulae and equations from the experimental results, the mole is selected as the standard amount of substance to measure the reaction rate, concentration, etc.
Thus in the present question, we know that Cuprous sulphide has a molecular formula of \[C{u_2}S\]. We can say that one mole of \[C{u^{2 + }}\] replaces two moles of \[C{u^ + }\] as depicted below:
\[C{u_2}S \to 2C{u^ + }{S^{2 - }}\;\;\;\;\;\;\;\]
(Given: Due to impurity of \[C{u^{2 + }}\] and \[C{u^ + }\] in the crystal, molecular formula becomes \[C{u_{1.95}}{S_{1.00}}\])
Now, let us suppose no. of moles of \[C{u^ + }\] be x and no. of moles of \[C{u^{2 + }}\] be y.
According to Neutrality, the equation can be written as follows:
$x + 2y = 2$ ………………… (1)
After incorporation of impurities, equation becomes as depicted below:
$x + y = 1.95$ …………….. (2)
Now, solving both equations (1) and (2), find out the values of x and y:
y = 0.05
x = 1.9
Therefore, \[C{u^{2 + }}\] = 0.05, but total given is 1.95, therefore:
Mole fraction of \[C{u^{2 + }}\]= $\dfrac{{0.05}}{{1.95}} = 0.0256$
Percentage of \[C{u^{2 + }}\](mole %) in the sample= $0.0256 \times 100 = 2.56$
Now, Percentage of \[C{u^ + }\] (mole %) in the sample= 100 - 2.56 = 97.44
Finally, we can calculate the Ratio of \[C{u^{2 + }}\] and \[C{u^ + }\]= $\dfrac{{2.56}}{{97.44}} = 1:38$

As a result, the correct answer is Option B i.e. the ratio of \[C{u^{2 + }}\]and \[C{u^ + }\] ion is 1 : 38.

Note: A crystallographically-distinct phase (i.e. mineral djurleite) also exists which has a stoichiometry \[C{u_{1.96}}S\] that is non-stoichiometric in the range \[C{u_{1.934}}S - C{u_{1.965}}S\]. It possesses a monoclinic structure having 248 copper atoms and 128 sulfur atoms in a unit cell. However, \[C{u_2}S\] and \[C{u_{1.96}}S\] have a similar appearance and thus, it is hard to differentiate one from the other.