# 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)

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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 $1L = 1000ml = 1000c{{m}^{3}}$ .