Question

How many atoms are in $33g$ of titanium ($Ti$)?

Answer 1

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 $1$.
${n_A}\, = \,\dfrac{{mass\,of\,A}}{{molecular\,mass\,of\,A}}$
${n_B}\, = \,\dfrac{{mass\,of\,B}}{{molecular\,mass\,of\,B}}$
${n_A}\, + {n_B}\, = \,1$