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Question: How do you convert \( 5.3 \times {10^{25}}\; \) molecules \( C{O_2} \) to moles?...

How do you convert 5.3×1025  5.3 \times {10^{25}}\; molecules CO2C{O_2} to moles?

Explanation

Solution

The mole concept is very significant and useful in chemistry. It is actually the base of stoichiometry and it provides the best option to express the amounts of reactants as well as products that are consumed and formed during a chemical reaction.

Complete answer:
To calculate the number of moles, we generally use the following formula:
Number of moles=Given mass Molecular mass of the given speciesNumber{\text{ }}of{\text{ }}moles = \dfrac{{Given{\text{ }}mass{\text{ }}}}{{Molecular{\text{ }}mass{\text{ }}of{\text{ }}the{\text{ }}given{\text{ }}species}}
We know that 1 mole of any substance contains 6.023×1023molecules6.023 \times {10^{23}}molecules
Thus, the number of molecules of any substance can be identified by multiplying the number of moles with Avogadro's number i.e. 6.023×10236.023 \times {10^{23}} . We can say:
Number of molecules=number of moles×6.023×1023Number{\text{ }}of{\text{ }}molecules = number{\text{ }}of{\text{ }}moles \times 6.023 \times {10^{23}}
In the question, we are given number of molecules of CO2C{O_2} i.e. 5.3×1025  5.3 \times {10^{25}}\; molecules.
If we substitute this value in the aforementioned formula of number of molecules, we can easily obtain the number of moles of CO2C{O_2} as depicted below:
5.3×1025  =number of moles×6.023×10235.3 \times {10^{25}}\; = number{\text{ }}of{\text{ }}moles \times 6.023 \times {10^{23}}
Now rearranging this equation, we will get the value of number of moles as shown below:
  number of moles=5.3×10256.023×1023=87.99≃88mol\;number{\text{ }}of{\text{ }}moles = \dfrac{{5.3 \times {{10}^{25}}}}{{6.023 \times {{10}^{23}}}} = 87.99 \simeq 88mol
Hence, 88 moles of CO2C{O_2} contain 5.3×1025  5.3 \times {10^{25}}\; molecules.

Additional information:
If we are provided with the given mass of the compound, we can calculate molecular mass of that compound by adding the relative atomic masses of each element present in that particular compound. Then using these two values, we can calculate the number of moles.

Note:
Avogadro's number was actually obtained by dividing charge of one mole of electrons by the charge of one single electron that equals 6.02214154×1023  6.02214154 \times {10^{23}}\; particles per mole. In order to convert moles into atoms, we can multiply the moles with Avogadro's number and if we want to convert atoms into moles, divide the number of atoms by Avogadro's number.