Question

A drop (0.05 mL) of 12.0 M HCl is spread over a sheet of thin aluminum foil. Assuming that the acid dissolves through the foil, the area is $x{\text{ }} \times {\text{ }}{10^{ - 1}}c{m^2}$ of the hole produced, then x is : (Density of Al = 2.70 $\dfrac{g}{{c{m^3}}}$; thickness of the foil = 0.10 mm)

Answer 1

To answer this question at first, the mass of aluminum should be calculated. Then according to the density, calculate the volume of the aluminum foil. Then from the volume find out the area of the foil. From the calculated value of the area, the value of the x can be calculated by comparing it with the given values.

Formula used: volume = area $\times$ thickness, density= mass/volume.

Complete step by step answer:
The equivalent mass of a substance can be explained as the number of parts by mass of the given chemical species which can combine with or displace 35.5 parts of Cl or 8.0 parts of O or 1.008 parts of H.
According to the question, the Meq. Of Al = Meq of HCl.
Therefore, the Meq. Of Al is, $12 \times 0.05 = 0.6$ .
Therefore, the mass of aluminum is 0.6 Meq. is, $\dfrac{{0.6 \times 9}}{{1000}} = 0.0054\,gm$ .
Now, the density is the ratio of mass to volume. So, the volume would be,
$\dfrac{{0.0054\,}}{{2.70}} = 0.002\,\,c{m^3}$.
According to the definition of the volume, volume = area $\times$ thickness.
Therefore, the area of the aluminum foil would be,

$$\dfrac{{0.002\,\,c{m^3}}}{{0.10\,\,mm}}\,\, \\\ = \dfrac{{0.002\,\,c{m^3}}}{{0.01\,\,cm}}\,\, \\\ = \dfrac{{0.002\,\,}}{{0.01\,\,}}\,c{m^2}\, \\\ = 0.2\,c{m^2}\, \\\$$

According to the question the area is, $x{\text{ }} \times {\text{ }}{10^{ - 1}}c{m^2}$ . So, the value of x is,

$$x \times {10^{ - 1}} = 0.2 \\\ or,x = 2 \\\$$

So, the value of the x is 2.

Note: Depending on the type of the chemical species under consideration, the formula for calculating the equivalent mass can be varied. The basic formula for calculating the equivalent mass of any chemical species can be done by dividing the sum of the masses of the number of atoms of the given chemical species by the key characteristic property of that species.