Question

$1.2 \times {10^ {24}}$ atoms of iron equals _______ moles.
(atomic number (Z) and atomic mass of iron, Fe is 26 and 56 respectively)
(a) 6
(b) 5
(c) 4
(d) 1.99

Answer 1

Avogadro's number is a very important relationship to remember: 1 mole=$6.022 \times {10^ {23}}$ atoms, molecules, protons, etc. To convert from moles to atoms, multiply the molar amount by Avogadro's number. To convert from atoms to moles, divide the atom amount by Avogadro's number (or multiply by its reciprocal).

Complete step by step answer:
We have been provided $1.2 \times {10^ {24}}$atoms of iron,
We need to convert atoms into moles. For that,
-Avogadro’s number is a very important relationship to remember: 1 mole =$6.022 \times {10^ {23}}$ atoms, molecules, protons, etc.
-To convert from moles to atoms, multiply the molar amount by Avogadro’s number.
-To convert from atoms to moles, divide the atom amount by Avogadro’s number (or multiply by its reciprocal).
Here, we have been given iron,
As we know molar mass of Fe= 56g/mol
1 mole= $6.022 \times {10^ {23}}$ atoms,
56 g= $6.022 \times {10^ {23}}$ atoms,
For 1 atom: 1 atom= $\dfrac {1} {{6.022 \times {{10} ^ {23}}}}$ moles,
So, for $1.2 \times {10^ {24}}$atoms: $\dfrac {1} {{6.022 \times {{10} ^ {23}}}} \times 1.2 \times {10^ {24}}$moles,
$1.2 \times {10^ {24}}$atoms=$1.99$moles.
So, we can say that $1.2 \times {10^ {24}}$atoms of iron equals 1.99 moles.
So, the correct answer is “Option D”.

Note: The charge on a mole of electrons had been known for some time and is the constant called the Faraday. If you divide the charge on a mole of electrons by the charge on a single electron you obtain a value of Avogadro's number $6.022 \times {10^ {23}}$ of particles per mole.