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# The density of liquid mercury is $13.6gc{{m}^{-3}}$ . How many moles of mercury are there in 1 litre of the metal?(Atomic mass of Hg = 200)

Last updated date: 20th Jun 2024
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Hint:. To solve this basic illustration, we need to have a basic idea about the density and its formula. Density of a substance is the mass of the same per litre of solution. This can simply be expressed as:
$Density=\dfrac{Mass}{Volume}$

Complete step by step answer:
Let us solve the given illustration directly,
We have,
Density of liquid mercury = $13.6gc{{m}^{-3}}$
Volume of mercury = 1 L
Atomic mass of mercury = 200 g/mol
As we have known,
$Density=\dfrac{Mass}{Volume}$
Mass of mercury can be found as:
$Mass=Density\times Volume$
Thus,
Mass of mercury = $13.6\times 1000 = 13600g$
Now,
The number of moles of mercury can be found out as;
Number of moles = $\dfrac{{{m}_{g}}}{{{m}_{m}}}$
where,
${{m}_{g}}$ = given mass
${{m}_{m}}$ = molecular mass
Number of moles = $\dfrac{13600g}{200g/mol}=68mol$
Therefore, there are 68 moles of mercury present.

Note: Do note that the unit conversions are important while solving such questions. Here, the important conversion is $1L = 1000ml = 1000c{{m}^{3}}$ .