Question

A partially dried clay mineral contains \[8%\] water. The original sample contained \[12%\] water and \[45%\] silica. The $%$ of silica in the partially dried sample in nearly:
A) $50%$
B) $49%$
C) $55%$
D) $47%$

Answer 1

Hint: While calculating the percentage composition of a substance by comparing the amount of it, at the original state of the sample and the final state of the sample, we need to assume the total amount of sample at first, especially if we are asked in terms of percentage. Then we would add all the values of the components in the original sample and then the values of the sample of the final state, in order to find out the amount of sample left after the change of state.Finally we determine the percentage composition of the asked component by applying the simple formula of percentage calculation.


Complete answer:
In order to solve this question we are going to assume that the total weight of the sample is $100g$, so that the calculations become a bit clearer. Now, it is being mentioned in the question that the original sample contains \[12%\] water and \[45%\] of silica. Since, we took $100g$ as the total sample, we can say that the original sample contained $12g$ of the water, and $45g$ of silica. If we add up these values we get $57g$ and so we are still left with $43g$ of the total sample.
Now if we consider the dried sample, it has $8%$ water, meaning $8g$ of water. So, the total weight of dried sample becomes $43+45+8g$ which becomes $96g$
Now the percentage of silica in the dried sample would be
$\dfrac{{{S}_{o}}}{M}\times 100$
Where ${{S}_{o}}$ is the weight of the silica in the original sample, and $M$ is the total mass of the sample after drying.
 $\dfrac{45}{96}\times 100=46.87%$

Which is approximately $47%$. So the most appropriate answer would be option D.

Note:The percentage of silica is calculated by using the mass of water and silica in the original sample, and then using it to calculate the total weight of the sample after drying. The percentage of silica is then calculated per total mass of the dried sample.