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Question: The number of moles in \(4 \times {10^{31}}\) atoms of iron are A) \(6.6 \times {10^7}\) B) \(3...

The number of moles in 4×10314 \times {10^{31}} atoms of iron are
A) 6.6×1076.6 \times {10^7}
B) 3.3×1073.3 \times {10^7}
C) 1014{10^{14}}
D) 8×10148 \times {10^{14}}

Explanation

Solution

We know that the relation between mole and Avogadro’s number is,
1 mol=6.022×10236.022 \times {10^{23}} atoms. Here, we have to use this relation to calculate the number of moles of iron in 4×10314 \times {10^{31}} atoms of iron.

Complete step by step answer:
We know that in one mole of anything, the number of atoms present is 6.022×10236.022 \times {10^{23}}. Now, we have to use the unitary method to calculate the number of moles of iron.
6.022×10236.022 \times {10^{23}} atoms of iron are present in=1 mole of iron
Therefore, 4×10314 \times {10^{31}} atoms of iron present in=4×10316.022×1023mol=0.6642×108=6.6×107 mol\dfrac{{4 \times {{10}^{31}}}}{{6.022 \times {{10}^{23}}}}{\rm{mol}} = 0.6642 \times {10^8} = 6.6 \times {10^7}\,{\rm{mol}}
Hence, the correct answer is option A.

Additional Information:
The mole or mol (abbreviation form) is the unit which measures the amount of substance present. A mole is the term that defines the number of carbon (C) atoms in 12 g of pure carbon. After so many years of experiment, it has been proved that a mole of anything contains 6.022×10236.022 \times {10^{23}} representative particles.
The number 6.022×10236.022 \times {10^{23}} is named in honor of the Italian physicist Amedeo Avogadro. The Avogadro's number aids in counting very small particles. Different kinds of particles, such as molecules, atoms, ions, electrons are representative particles. One mole of anything consists of 6.022×10236.022 \times {10^{23}} representative particles. For example, one mole of oxygen consists of 6.022×10236.022 \times {10^{23}} molecules of oxygen. Hence, the relation between mole and Avogadro’s number is 1 mol=6.022×10236.022 \times {10^{23}} atoms.

Note:
There is a close relation between moles and dozen. A dozen always represents twelve articles. They may be orange, apple, banana etc. In a similar manner, a mole represents 6.022×10236.022 \times {10^{23}} particles which may be atoms, molecules, ions, electrons, protons etc. Therefore, a mole is often called a chemist's dozen.