Question

How many atoms are in \[33g\] of titanium (\[Ti\])?

Answer 1

Hint: Titanium is denoted with the symbols of Ti having the atomic number \[22\] and the atomic mass \[47.867{\text{ }}g/mol\]. It is one of the transition metals which is lustrous with silver colour. It is having low density and high strength. A mole is defined as \[6.02214076 \times {10^{23}}\] of a chemical unit in the terms of ions, atoms, molecules, etc.

Complete step by step answer:
A mole is a unit measurement for the amount of substance in the international system of units i.e., SI unit. A mole of a particle or a mole of substances is defined as \[6.02214076 \times {10^{23}}\] of a chemical unit, that can be ions, atoms, molecules, etc. Originally it was defined as the number of atoms in \[12{\text{ }}g\] of carbon-12.
The \[1\,g\] of the atom will be equal to \[1\]mole.
In equation, \[1\,g\] of atom \[ = \,\,1\,\]mole
Since, \[1\]mole contains Avogadro’s number (\[{N_A}\] ) of atoms.
So, \[1\,mole\, = \,6.022\, \times \,{10^{23}}\,atoms\]
Therefore, for \[1\] atom will be;
\[1\,atom\, = \,\dfrac{1}{{6.022\, \times \,{{10}^{23}}}}\,g\,atoms\]
So, the answer will be;
\[1\,atom\, = 1.66\, \times \,{10^{ - 24}}\,g\,atoms\]

To calculate the number of moles;
Let’s use the equation;
Number of moles, \[n\, = \,\dfrac{{mass}}{{molecular\,mass}}\]
The given mass of titanium (\[Ti\])=\[33{\text{ }}g\]
The molecular mass of titanium (\[Ti\]) = \[47.867{\text{ }}g/mol\]
Substitute the values in above equation,
\[n\, = \,\dfrac{{33}}{{47.867}}\]
So, the number of moles will be;
\[n\, = \,0.692\]
\[ = \,\dfrac{g}{{g\,mo{l^{ - 1}}}}\]
\[ = \,\dfrac{1}{{mo{l^{ - 1}}}}\,\]
\[ = \,\dfrac{1}{{\dfrac{1}{{mol}}}}\,\]
\[ = mo\not l\]
We have to multiply with Avogadro's number to get the atoms.
Now, let’s calculate the number of atoms present in \[33{\text{ }}g\] of titanium
\[ = \,0.69\, \times \,6.023\, \times \,{10^{23}}\]
\[ = \,4.15\, \times \,{10^{23}}\] atoms

So, the answer obtained will be, \[\,4.15\, \times \,{10^{23}}\] atoms are present in \[33{\text{ }}g\] of titanium.

Note: If a compound is having the mass, we can calculate the moles by using the formula of moles, either it is for one molecule or the compound. If a compound is having \[A\] and \[B\] molecules then the sum of the moles will be \[1\].
\[{n_A}\, = \,\dfrac{{mass\,of\,A}}{{molecular\,mass\,of\,A}}\]
\[{n_B}\, = \,\dfrac{{mass\,of\,B}}{{molecular\,mass\,of\,B}}\]
\[{n_A}\, + {n_B}\, = \,1\]