Question

What is the mass of nickel in kg, that would give $9.2 \times {10^{25}}$ atoms of nickel (use mole concept)?

Answer 1

To solve the question we need to understand the mole concept. Mole is the fundamental unit for the measurement or it is the S.I unit of the amount of substance. It gives the number of atoms or molecules in the substance. 1 mole of a particular substance contains $6.022 \times {10^{23}}$ atoms or molecules.

Complete answer:
To solve the question let us look at the following relations-
(A) 1 Mole=Atomic mass or Molecular mass or formula unit mass
For Example- 1 mole of carbon=12 g
(B) 1 Mole= $6.022 \times {10^{23}}$ atoms or molecules. This number is called the Avogadro number.
For Example- 1mole of hydrogen molecules= $6.022 \times {10^{23}}$ hydrogen molecules
(C) Mole is calculated as given mass/molar mass.
(D) Number of moles (n) is given as $\dfrac{N}{{{N_A}}}$ where N is the total number of atoms or molecules present and NA is the Avogadro number.
In the question, we are given-
Number of atoms (N) $= 9.2 \times {10^{25}}$ atoms of nickel
We are asked to find the mass of nickel in kg,
Let us first find the number of moles by the formula- $n = \dfrac{N}{{{N_A}}}$
Putting all the values we have-
$\Rightarrow n = \dfrac{{9.2 \times {{10}^{25}}}}{{6.022 \times {{10}^{23}}}}$
Now using the equation number of moles=given mass/molar mass
Given mass=Number of moles * molar mass
Molar mass of nickel=58.7g/mole.
Given $mass = \dfrac{{9.2 \times {{10}^{25}}}}{{6.022 \times {{10}^{23}}/mol}} \times 58.7g/mole = 8967.7g$
Since we are asked mass in kg we get approximately 9 Kg. (1 kg=1000 g)
We can also solve the question using the unitary method. In this case, we know that –
$1\;mole = 6.022 \times {10^{23}} atoms=58.7\;g\;of\;nickel$
So 1 atom will contain $\dfrac{{58.7}}{{6.022 \times {{10}^{23}}}}$ g of nickel
So $9.2 \times {10^{25}}$ atoms will contain= $\dfrac{{58.7}}{{6.022 \times {{10}^{23}}}} \times 9.2 \times {10^{25}}$ =8967.7g=9kg.

Note:
It is interesting to note that it was Wilhelm Ostwald who first introduced the concept of mole in 1893. Since we cannot see the subatomic particles like atoms and molecules the concept of the mole is very important to convert grams to mole and moles to grams and allows chemists to work on microunits.