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Question: \(C{u_2}S\) and \({M_2}S\) are isomorphous in which percentage of Sulphur is 20.14%. and 12.94% resp...

Cu2SC{u_2}S and M2S{M_2}S are isomorphous in which percentage of Sulphur is 20.14%. and 12.94% respectively. The atomic weight of M is:
A. 208
B. 108
C. 112
D. 106

Explanation

Solution

To calculate the atomic weight of M, first we need to find the mass of Sulphur. The formula used for the calculation is mass percentage. Mass percentage is calculated by dividing the mass of compound x with total mass of compound x and y multiplied by 100.

Complete step by step answer:
The percentage of Sulphur in Cu2SC{u_2}Sis 20.14 %
The percentage of Sulphur in M2S{M_2}Sis 12.94%
The atomic weight of Cu is 63.5.
The mass percentage is calculated by mass of compound x divided by total mass of compound x and compound y multiplied with 100.
The formula for calculating the mass percentage is shown below.
mass%=mass of  xmass  of  x+mass  of  y×100mass\% = \dfrac{{mass\,of\;x}}{{mass\;of\;x + mass\;of\;y}} \times 100
Where,
x is the mass of compound x.
y is the mass of compound y.
Let assume that the x be the mass of Sulphur.
In Cu2SC{u_2}S, from two mole of Cu one mole of Sulphur is present. Therefore the mass of copper will be 127.
To calculate the mass of Sulphur substitute, the values in the equation.
⇒20.14%=mass of  xmass  of  x+127×100\Rightarrow 20.14\% = \dfrac{{mass\,of\;x}}{{mass\;of\;x + 127}} \times 100
⇒100x=2557.78+20.14x\Rightarrow 100x = 2557.78 + 20.14x
⇒x=2557.7879.86\Rightarrow x = \dfrac{{2557.78}}{{79.86}}
⇒x=32\Rightarrow x = 32
Let assume that the atomic weight of silver is W.
In M2S{M_2}S, for two mole of M one mole of Sulphur is present.
To calculate the atomic weight of M, substitute the values in the equation.
⇒12.94%=3232+2W×100\Rightarrow 12.94\% = \dfrac{{32}}{{32 + 2W}} \times 100
⇒12.94%=160016+W\Rightarrow 12.94\% = \dfrac{{1600}}{{16 + W}}
⇒\Rightarrow 1600= 12.94W + 12.94 ×\times 16
⇒\Rightarrow 12.94W = 1600 - 12.94 ×\times 16
⇒12.94W=1392.96\Rightarrow 12.94W = 1392.96
⇒W=1392.9612.94\Rightarrow W = \dfrac{{1392.96}}{{12.94}}
⇒W=108g\Rightarrow W = 108g
Thus, the atomic weight of M is 108g.
So, the correct answer is “Option B”.

Note:
Make sure that in the given compounds for every 2 mole of metal, 1 mole of Sulphur is present, it will help in determining the mass of metal with the help of its atomic weight.