Question

The density of liquid mercury is $13.6g/c{{m}^{3}}$. How many moles of mercury are there in 1 litre of the metal? (atomic mass of Hg = 200 g/mol)
(A) 55
(B) 13.6
(C) 68
(D) none of these.

Answer 1

To calculate number of moles of given substance, we should use the product of volume and density to determine the given mass of the same. Units must be considered wisely while solving such problems.

Complete step by step solution:
Let us study about the density of any substance and some basic mole concepts.
Density- Density depends upon the mass and volume of a substance. It is directly proportional to mass quantities and inversely proportional to volume quantities, resulting into the definition as, Density of any substance is its mass per volume.
Number of moles- The number of moles is the ratio of similar quantities and hence is unitless. The ratio of given mass of any substance to the atomic mass of the same gives the moles of that substance.
Illustration- Given that, Density of liquid mercury = $13.6g/c{{m}^{3}}$
Atomic mass of mercury = 200 g/mol
Now, We know that
1 L = 1000 $c{{m}^{3}}$
Thus, 1 L of metal has 13600 gm of mercury.
Therefore, The number of moles of mercury present in metal = $\dfrac{13600g}{200g/mol}$
= 68 mol.

Hence, option (C) is correct.

Note: Do note that
1 L corresponds to 1000 $c{{m}^{3}}$. Confusion in unit conversion can result in chaos in further problem solving.