Question

What is the molarity of pure water?

Answer 1

Hint: The standard state for a liquid is the pure liquid, so the standard state of water is pure water. There will not be any impurities present in the water which can alter its concentration. In dilute aqueous solutions, the concentration of water is very close 1.

Complete step by step solution:
Molarity is defined as the moles of solute dissolved in one litre of solution. Molarity decreases with an increase in temperature.
\[Molarity=\dfrac{Number\,of\,moles\,of\,solute}{Volume\,of\,solution\,in\,litre}\]
We know that the density of water is l kg/L. Let us take one litre of water.
We know the formula for mass is given by:
\[Mass=density\times volume\]
Therefore, the mass of 1L of water will be:
\[\begin{align}
  & Mass\,of\,water=1\dfrac{kg}{L}\times 1L \\
 & \,\,\,\,\,\,\,\,\,\,\,\,\,=1\,kg=1000g \\
\end{align}\]
Now we will calculate the number of moles by dividing the mass of the substance in grams by its molar mass. This will give you the number of moles of that substance that are in the specified mass.
\[Number\,of\,moles\,=\,\dfrac{Given\,mass}{Molar\,mass}\]
We can calculate the molar mass of water as:
One mole of \[{{H}_{2}}O\] is made up of 2 moles of Hydrogen atoms and 1 mole of Oxygen atom.
Mass of 1 mole of Hydrogen atoms= 1 g /mol
Mass of 1mole of Oxygen atoms = 16 g/mol
Mass of two moles of Hydrogen atoms = 2x 1 g/mol = 2 g/mol.
Mass of one mole of Oxygen atoms = 1 x 16 g /mol
Mass of one mole of water = 2 g/mol + 16 g/mol = 18 g/mol.
\[Number\,of\,moles=\dfrac{1000g}{18g/mol}=55.5\,5\,mol\]
Now we have both the number of moles of water and volume of water. So, from here we can calculate molarity from the given formula.
\[Molarity=\dfrac{55.5\,mol}{1L}=55.55\,M\]

Note: Similarly, we can calculate Molality, defined as the number of moles of solute dissolved in 1 kg of solute. It is independent of temperature.
Formula for calculating molality,
\[\begin{align}
  & Molality=\dfrac{Number\,of\,Moles}{Weight\,of\,sovent\,in\,Kg} \\
 & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=\dfrac{55.55\,mol}{1\,kg}=55.55\,m \\
\end{align}\]