Question

How many atoms are in $0.075$ mole of titanium?

Answer 1

The mole is widely used in chemistry as a convenient way to express amounts of reactants and products of chemical reactions. It is a fundamental unit which helps to calculate a big number. The mole is essentially a count of particles. The mole designates an extremely large number of units, $6.02214076 \times {10^{23}}$.

Complete step by step answer:
A mole is derived from a Greeks word called mol. Which means a heap or pile. It is used to calculate a big number which is difficult to calculate in real numbers.
In the international system of units called the s1 system, mole is one of the fundamental units which help us to calculate the big number.
It is also called Avogadro’s number in respect of Amadeo Avogadro and one mole of any substance (atoms, ions, molecules, electron, neutron and proton) is equal to 1 mole $= 6.022 \times {10^{23}}$ particles.
In chemistry, mole is widely used to calculate the amount of substance formed, volume of gas released at standard temperature and pressure condition called STP, number of particles or molecules formed during a chemical reaction.
It also helps us to calculate the gram molecular mass and gram atomic mass of a substance in reference of $\dfrac{1}{{12}}th$ of $C - 12$.
We have to find the number of atoms in $0.075$ mole of titanium.
One mole of atom contains $N_A$ number of atoms
Where, $N_A$=$6.022 \times {10^{23}}mo{l^{ - 1}}$
No. of atoms $= 0.075 \times N_A$ titanium atoms
So $0.075$ mole contain $$$$$= 0.075 \times 6.022 \times {10^{23}}$
$= 0.45165 \times {10^{23}}$

Final Answer, $0.075$ mole of titanium atom contain $= 0.45165 \times {10^{23}}$

Note: Mole can also be find out by many ways
Number of moles $= \dfrac{{mass{\text{ }}of{\text{ }}given{\text{ }}atom}}{{gram{\text{ }}atomic{\text{ }}mass\;}}$
Number of moles $= \dfrac{{mass{\text{ }}of{\text{ }}given{\text{ }}molecule}}{{gram{\text{ }}molecular\;}}$
Number of moles $= \dfrac{{given{\text{ }}volume{\text{ }}of{\text{ }}gas}}{{molar{\text{ }}volume{\text{ }}of{\text{ }}at{\text{ }}STP22.4litre}}$