Question

The number of molecules in $2.5$ moles of water is:
a.) $6.023 \times {10^{23}}$ molecules
b.) $12.046 \times {10^{23}}$ molecules
c.) $2.012 \times {10^{23}}$ molecules
d.) $15 \times {10^{23}}$ molecules

Answer 1

Hint: 1 mole of any entity is the amount of substance that contains exactly $6.02214076 \times {10^{23}}$ atoms, molecules, or ions. So, the number of molecules in 2.5 moles of water $({H_2}O)$ molecules $ = 2.5 \times 6.023 \times {10^{23}} = 15.076 \times {10^{23}} \approx 15 \times {10^{23}}$

Complete step by step answer:
To understand the mathematical calculations, it is necessary to first understand the concept of mole (i.e. the mole concept).
Mole concept – 1 mole of any entity (it can be atoms, molecules, or ions) is the amount of substance that contains exactly $6.023 \times {10^{23}}$ atoms, molecules, or ions.
So, for example, 1 mole of $O$ atoms contains $6.023 \times {10^{23}}$ atoms of oxygen. 1 mole of $C{O_2}$ molecules contains $6.023 \times {10^{23}}$ molecules of carbon dioxide and 1 mole of ${H^ + }$ ions will contain $6.023 \times {10^{23}}$ hydrogen ions.
Let’s also discuss the mole concept with respect to the weight of the substance. So the amount of a substance that weighs equal to the molar mass of that substance in grams contains 1 mole of that substance or $6.023 \times {10^{23}}$ entities of that substance.
This concept can be a bit confusing, so let’s take an example of ${O_2}$ molecules.
16 grams of ${O_2}$ molecules will contain $6.023 \times {10^{23}}$ molecules of ${O_2}$ as the molar mass of ${O_2}$ molecule is 16 amu (1 amu is exactly $\dfrac{1}{{12}}$ of the mass of a carbon-12 atom).
Now in the problem given to us, we have to calculate the number of water $({H_2}O)$ molecules in 2.5 moles of water.
As we already know from the earlier discussion that 1 mole of any molecule contains $6.023 \times {10^{23}}$ molecules of that substance, so the number of molecules in 2.5 moles will be
Number of molecules in 2.5 moles of water $({H_2}O)$ molecules $ = 2.5 \times 6.023 \times {10^{23}}$
Number of molecules in 2.5 moles of water $({H_2}O)$ molecules $ = 15.076 \times {10^{23}} \approx 15 \times {10^{23}}$ molecules
So, 2.5 moles of water will contain $15 \times {10^{23}}$ molecules of water.
So, the correct answer is “Option D”.

Note: In the solution above we discussed the mole concept. At first glance, it does not seem to be very important, but the mole concept is like the backbone of all laboratory experiments. With the mole concept we can even measure how many molecules, atom is in a sample and predict the rate of reaction for any reaction.