Question

A sample of \[{C_3}{H_8}\] has \[8.48 \times {10^{24}}H\] atoms. How many carbon atoms does the sample contain?

Answer 1

Hint: A mole is one of the fundamental units which helps to calculate a big number. In any chemical reaction, the number of mole ratio of reactant and product is always fixed i.e., we always use a fixed number of molecules of reactant to form a fixed number of moles of product.

Complete step by step answer:
A mole is derived from a Greek word called Mol which means a heap or a pile. It is used to calculate a big number which is difficult to calculate in real terms. In the international System of Units called SI system, mole is one of the fundamental units which help us to calculate the big numbers. It is also called Avogadro’s number in respect of Amadeo Avogadro and one mole of any substance (atom, 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 $1/{12^{th}}\;of\;C - 12.$
Given: Number of H-atom in ${C_3}{H_8}$ sample $ = 8.48 \times {10^{24}}$ H-atom
Formula used: - First we find the number of moles of ${C_3}{H_8}$ of the given sample
Number of moles of H-atom $ = $ Given number of atoms $/6.022 \times {10^{23}}$
Number of moles of H-atom $ = 8.48 \times {10^{24}}$ H-atom $/6.022 \times {10^{23}}$
Number of moles of H-atom $ = 14.08$ moles
In the given molecule,
\[8\] mole of H atom combines with $3 \times {10^{23}}$ C-atom
So, \[14.08\] mole of H-atom combines with $\dfrac{{3 \times {{10}^{23}} \times 14.08}}{8}$ C-atom
$ = 5.28 \times {10^{23}}$ C-atom
Final answer:
Number of C-atom $ - 5.28 \times {10^{23}}$ C-atom

Note:
Mole can also be found in many ways. Number of moles $ = $ mass of given atom $/$ gram atomic mass
Number of moles $ = $ mass of given molecule $/$ gram molecular mass
Number of moles $ = $ Given volume of gas at STP $/$ molar volume of \[22.4\] Liter