Question

How many atoms or molecules are present in $1.0mol$ of $Au$?.

Answer 1

Hint: As we are well aware with the term mole which is given as the ratio of the given mass of any substance or compound to the molecular mass of the given substance or compound. We can calculate it by knowing the mass and molecular mass of the compound. We also know the moles are directly related to the number of atoms as well as molecules and volume of a substance.

Formula used: $moles \times {N_A} = no.of\;atoms\;or\;molecules$

Complete step-by-step answer:
As we already know the mole concept where a mole is defined when mass of a substance is divided by the molecular mass of that substance. It is expressed as shown below:
$moles = \dfrac{{mass}}{{molecular\;mass}}$

Now, along with moles, we can also calculate the other parameters such as the volume of any substance at NTP or STP, number of atoms, number of molecules and many more in a given mass of any substance using the below formula:
$\Rightarrow moles = \dfrac{{mass}}{{molecular\;mass}} = \dfrac{{vol.\;at\;STP}}{{22.4L}} = \dfrac{{no.of\;molecules\;or\;atoms}}{{{N_A}}}$
Where ${N_A}$ is Avogadro’s number.

So, using the above relation between moles and number of atoms and moles and number molecules we can easily identify the atoms or molecules of $Au$ in given number of moles using:
$\Rightarrow moles = \dfrac{{no.of\;atoms\;or\;molecules}}{{{N_A}}}$
We are given with $1.0mol$ of $Au$, so after putting it in the formula we would get:
$\Rightarrow moles \times {N_A} = no.of\;atoms\;or\;molecules$
$\Rightarrow no.of\;atoms = 1.0 \times 6.022 \times {10^{23}}$
$\Rightarrow no.of\;atoms = 6.022 \times {10^{23}}$
Similarly, we can calculate the number of molecules present in $1.0mol$ of $Au$ and they will be equivalent to:
$\Rightarrow no.of\;molecules = 1.0 \times 6.022 \times {10^{23}}$
$\Rightarrow no.of\;molecules = 6.022 \times {10^{23}}$

Therefore the correct answer is that $1.0mol$ of $Au$ contains the similar number of atoms or molecules as the Avogadro’s number.

Note: Always remember that the ratio of mass to the molecular mass is equivalent to its number of moles which in turn is equivalent to the ratio of number of atoms or number of molecules to the Avogadro’s number. We can also calculate the volume of a substance if we know its number of moles.