Question

The volume occupied by one molecule of water at 4°C is:
A. \[3\times {{10}^{-23}}\]cc
B. $3\times {{10}^{23}}$cc
C. $3\times {{10}^{-24}}$cc
D. $3\times {{10}^{24}}$cc

Answer 1

Hint: We should know that the density of water at 4°Celsius is one gram per cubic centimetre. By knowing water density we can easily calculate volume occupied by water molecules at 4°Celsius. Keep in mind that in the given question the volume of one molecule of water at 4° Celsius should be calculated. Density should be calculated from one molecule of water.

Complete answer:
As we know the following thing about our question.
Density of water at 4°Celsius is one gram per cubic centimetre
Density (ρ) = \[\dfrac{Mass}{Volume}\]
Density of water (ρ) = \[\dfrac{Molar\,mass\,of\,water}{Density\,of\,water\,at\,given\,temperature}\]
Molar mass of water (M) = \[18\dfrac{gram}{mole}\]
First we will find the molar volume of water and then the value of the volume of one molecule.
Molar volume = \[\dfrac{Molar\,mass}{Density}\]
So by putting up the values, we get
Molar volume of water will be= \[18\dfrac{c{{m}^{3}}}{mole}\]
But as in the question give, we need to find volume of one mole of water at 4°C. So as we know that,
Volume of one molecule of water is= \[\] \[\dfrac{Molar\,volume}{Avogadro\,Number}\] (Equation one)
As we found out that, Molar volume of water is \[18\dfrac{c{{m}^{3}}}{mole}\]
An Avogadro number is $6.022\times {{10}^{23}}$.
By putting the value of molar volume and Avogadro number in equation one, we get..

Volume of one molecule of water is=
\[\dfrac{Molar\,Volume}{Avogadro\,Number}=\dfrac{18}{6.022\times {{10}^{23}}}=~2.989\times {{10}^{-23}}\]\[\sim 3\times {{10}^{-23}}\]cc

So our correct option will be (A).

Note:
1. Always keep a check on units carefully. Because unit conversion is important in these types of questions.
2. Always check in questions about what is asked, because sometimes there is a mention about the number of molecules so keep an eye on these minor details.
3. We should have knowledge of the density of different liquids like gasoline, oil, alcohol. Because it makes it easy to solve this type of question.
4. Cross verify the options.