Question

What mass of gold, \[{\text{Au}}\], contains the same number of atoms \[{\text{9g}}\] of aluminium, \[{\text{Al}}\]?

Answer 1

Hint: As we know that gold is one of the transition elements in the periodic table. The atomic number of gold is \[79\] and the mass number of gold is \[196.967\]. We have to know that the symbol of gold is \[{\text{Au}}\]. Aluminium is one of the metallic elements in the periodic table. The atomic number of aluminium is \[13\] and the mass number of aluminium is \[26.982\] . The symbol of Aluminium is \[{\text{Al}}\].

Formula used: The mole is defined as the given mass of the atom is divided by the atomic weight of the atom.
\[{\text{Moles = }}\dfrac{{{\text{given weight of the atom}}}}{{{\text{atomic weight of the atom}}}}\]
The number of atoms of the element is equal to the number of moles of the atom multiplied by Avogadro’s number. The numerical value of Avogadro’s number is \[6.022 \times {10^{23}}\].
\[{\text{The Number Of Atoms = number of moles \times 6}}{\text{.022 \times 1}}{{\text{0}}^{{\text{23}}}}\]

Complete step by step answer:
The given weight of aluminium is \[{\text{9g}}\] and the atomic weight of aluminium is \[{\text{26}}{\text{.982g}}\]
The number of moles of aluminium in given weight,
\[{\text{Moles = }}\dfrac{{{\text{Weight of the given atom}}}}{{{\text{Atomic weight of the atom}}}}\]
Now we can substitute the known values we get,
\[ = \frac{9}{{26.982}}\]
On simplification we get,
\[ \Rightarrow Moles = 0.3335\]
Hence, \[0.3335\] moles of aluminium present in the given weight.
Calculate the number of atoms in the given weight of aluminium
${\text{The number atoms}} = {\text{Number of moles}} \times 6.022 \times {10^{23}}$ Now we can substitute the known values we get
\[ = 0.3335 \times 6.022 \times {10^{23}}\]
On simplification we get,
\[{\text{The number of atoms}} = 2.0 \times {10^{23}}\]
Hence, \[2.0 \times {10^{23}}\] atoms of aluminium present in \[{\text{9g}}\]of aluminium.
Calculate the number of moles of \[2.0 \times {10^{23}}\] atoms of gold.
\[{\text{The Number Of Atoms = number of moles \times 6}}{\text{.022 \times 1}}{{\text{0}}^{{\text{23}}}}\]
We change the formula for our need,
\[{\text{number of moles = }}\dfrac{{{\text{The Number Of Atoms}}}}{{{\text{6}}{\text{.022 \times 1}}{{\text{0}}^{{\text{23}}}}}}\]
On substituting the known values we get,
\[ \Rightarrow {\text{Number of moles}} = \dfrac{{2.0 \times {{10}^{23}}}}{{6.022 \times {{10}^{23}}}}\]
\[ \Rightarrow {\text{Number of moles}} = 0.3335\]
Hence, \[0.3335\] moles of gold present in \[2.0 \times {10^{23}}\]atoms of gold.
Calculate the weight of gold in \[0.3335\] moles of gold,
\[{\text{Moles = }}\dfrac{{{\text{given weight of the atom}}}}{{{\text{atomic weight of the atom}}}}\]
We change formula for our need,
\[{\text{Given Weight Of The Atom = number of moles}} \times {\text{atomic weight of the atom}}\]
The atomic weight of gold is \[196.967g\]
\[ = 0.3335 \times 196.967\]
On simplification we get,
\[ = 65.69\]
Hence, \[65.69g\] of gold present in \[0.3335\] moles.

Therefore, \[65.69g\] of gold, \[{\text{Au}}\], contains the same number of atoms \[{\text{9g}}\] of aluminium, \[{\text{Al}}\].

Note: We have to know that the mole is one of the important units in chemistry. All the chemical reactions are expressed in terms of the moles of the reactant and product. If one reaction is completed or not also determined by the moles of the reactant and product. Aluminium and gold are useful metals for human life. Aluminium is used for household things and other uses. Gold is mainly used for ornaments and medicine.