Question

The density of mercury is 13.6 g/ cm$^{3}$. Estimate the b value. Atomic mass of Hg=200.
A.29.41 cm$^{3}$
B.58.82 cm$^{3}$
C.98.82 cm$^{3}$
D.None of these

Answer 1

Hint: The b value is related to the degree of diffusion. We are given with the density of mercury, and the molar mass of mercury. By applying the mole concept in the terms of volume as density is indirectly proportional to volume, the b value can be estimated.
Complete step by step answer:
Firstly, if we see the molar mass of mercury is 200 g / mole, and the density is 13.6 g/ cm$^{3}$.
Now, we know density is directly proportional to the molar mass, or mass. It can be written as D= $\dfrac{M}{V}$.
Thus, we can say that 1 mole of mercury will occupy a volume of 14.75 cm$^{3}$/mol. We calculated this by$\dfrac{200}{13.6}$. It represents the $\dfrac{M}{D}$.
We get the value of 14.75 cm$^{3}$/mol, it is the molar volume of mercury.
Now, if we talk about the b value, it is 4 times the molar volume. Thus the obtained value of molar volume can be multiplied by 4 to achieve the estimated value of b, i.e. 4 $\times$ 14.75 cm$^{3}$/mol = 58.87 cm$^{3}$/mol (approximately).

Therefore, the value of b is 58.87 cm$^{3}$ /mol. The correct option is B.

Note: Don’t get confused about how to solve the mole concept. Simply apply the formula of density in the terms of molar mass, and volume. From the density formula, the volume can be calculated, and the value of b is found by doing the 4 times of molar volume.