Molar Concentration of Water in Pure Water – Detailed Step-by-Step Calculation

Correct Answer: 55.5 M

How to Calculate the Molar Concentration of Water in Pure Water

The molar concentration of water in pure water can be calculated by determining how many moles of water are present in one litre of pure water. Although water is normally considered a solvent, pure liquid water itself has a definite molar concentration. To calculate this value, we need the density of pure water and the molar mass of H₂O.

Molar concentration, also called molarity, represents the number of moles of a substance present per litre of solution. Therefore, the molarity of pure water can be determined by calculating the number of moles of H₂O present in one litre of water.

Step-by-Step Calculation of the Molarity of Pure Water

Step 1: Write the Density of Pure Water

The density of pure water is approximately:

Density of water = 1 g mL⁻¹

Since one litre contains 1000 mL, the mass of one litre of pure water can be calculated as:

Mass = Density × Volume

Mass of 1 L water = 1 g mL⁻¹ × 1000 mL

Mass of 1 L water = 1000 g

Thus, one litre of pure water has a mass of approximately 1000 g.

Step 2: Calculate the Molar Mass of Water

The molecular formula of water is H₂O. Each water molecule contains two hydrogen atoms and one oxygen atom. Using the approximate atomic masses of hydrogen and oxygen, the molar mass can be calculated as follows:

Molar mass of H₂O = 2(1) + 16

Molar mass of H₂O = 18 g mol⁻¹

Therefore, one mole of water has a mass of approximately 18 g.

Step 3: Calculate the Number of Moles of Water

The number of moles is calculated by dividing the given mass by the molar mass:

Number of moles = Mass / Molar mass

For one litre of pure water:

Number of moles of H₂O = 1000 g / 18 g mol⁻¹

Number of moles of H₂O = 55.555… mol

Thus, approximately 55.555 moles of water are present in one litre of pure water.

Step 4: Calculate the Molar Concentration

Molarity is defined as the number of moles of solute or substance present per litre of solution:

Molarity (M) = Number of moles / Volume in litres

Since 55.555 moles of water are present in a volume of 1 litre:

Molarity of pure water = 55.555 mol / 1 L

Molarity of pure water = 55.555 M

The question asks for the answer rounded off to one decimal place. Therefore:

Molar concentration of pure water = 55.5 M

Direct Formula for Calculating the Molarity of Pure Water

The same result can also be obtained directly by using the relationship between density, molar mass and molarity:

Molarity = (Density × 1000) / Molar mass

Substituting the values for pure water:

Molarity = (1 × 1000) / 18

Molarity = 55.555… M

After rounding off to one decimal place:

Molarity = 55.5 M

Why Is the Concentration of Pure Water 55.5 M?

The value 55.5 M means that approximately 55.5 moles of H₂O molecules are present in every litre of pure water. This high molar concentration results from the relatively small molar mass of water, which is only about 18 g mol⁻¹, while one litre of water has a mass of approximately 1000 g.

Dividing the mass of one litre of water by its molar mass gives the total number of moles present in that litre. Therefore, the molarity of pure water is approximately 55.5 mol L⁻¹, commonly written as 55.5 M.

Final Answer

One litre of pure water has a mass of approximately 1000 g, and the molar mass of H₂O is approximately 18 g mol⁻¹. Therefore, the number of moles of water present in one litre is:

1000 / 18 = 55.555… mol

Hence, after rounding off to one decimal place, the molar concentration of water in pure water is 55.5 M.

Correct Answer: 55.5 M