Question

The density of water is 1g/mL. Assuming that there are no interspaces between water molecules in liquid water, the volume of water molecule is
A.$1.5 X {10^{ - 23}}$ mL
B.$6 X {10^{ - 23}}$ mL
C.$3 X {10^{ - 23}}$ mL
D.$3 X {10^{ - 22}}$ mL

Answer 1

The formula of density is ${\text{Density = }}\dfrac{{{\text{mass}}}}{{{\text{volume}}}}$ .
By knowing the formula of density and number of molecules, volume can be calculated. From the given density, the relation between mass and volume can be found out.

Complete step by step answer:
From the question, we have the density of water as 1 g/mL. We know the relation between density, mass and volume. ${\text{Density = }}\dfrac{{{\text{mass}}}}{{{\text{volume}}}}$ .
So, it means that mass is 1 gram for 1 mL of the water.
We know the equation to find the number of molecules. 1 mole of any substance in grams is equal to $6.022 X {10^{23}}$ (Avogadro’s Number)
Thus, we need to find the number of molecules in 1 gram of water.
No. of molecules in 1 g of water = $\dfrac{{{\text{1 X 6}}{\text{.022 X 1}}{{\text{0}}^{{\text{23}}}}}}{{{\text{18}}}}$
Here, 18 is the molar mass of water. It can be written as:
Molar mass of water = 2 (mass of hydrogen) + 1 (mass of oxygen)
Molar mass = 2 (1) + 1 (16)
Molar mass of water = 18 g
As we discussed above, mass is 1 gram for 1 mL of the water (where density is 1 )
Therefore, No. of molecules in 1 mL of water = $\dfrac{{{\text{1 X 6}}{\text{.022 X 1}}{{\text{0}}^{{\text{23}}}}}}{{{\text{18}}}}$
Now, let us find the volume of these molecules. It can be written as:
Volume of $\dfrac{{{\text{1 X 6}}{\text{.022 X 1}}{{\text{0}}^{{\text{23}}}}}}{{{\text{18}}}}$molecules = 1 mL
So, volume of 1 mL = $\dfrac{1}{{\dfrac{{6.022 X {{10}^{23}}}}{{18}}}}$
Volume $= \dfrac{{18}}{{6.022 X {{10}^{23}}}}$
Volume $= 3 X {10^{ - 23}}mL$
Hence, the correct answer is Option (C)

Note:
1 mole of a substance is the molecular mass in grams is equal to the Avogadro’s number. The equation of density is ${\text{d = }}\dfrac{{\text{m}}}{{\text{v}}}$, where d is the density, m is the mass and v is the volume. There could be a confusion between option C and option D because when the power to a number in the denominator will change into opposite when taken to the numerator. So, the answer will be $= 3 X {10^{ - 23}}mL$.