Water is a unique material in that the density of the solid is lower than the de
ID: 1006401 • Letter: W
Question
Water is a unique material in that the density of the solid is lower than the density of the liquid (which is why ice forms at the top of a pond and why ice floats in our drinks). If the density for ice at 0 degree C is 0.917 g/mL and the density for water at 0 degree C is 0.999 g/mL., what is the calculated free space (as %) for each of these materials? you will need to estimate the volume of water as the sum of 2 H atoms and 1 O atom with radii of 37 and 66 pm respectively. note that you will also have to assume a quantity of water to perform this exercise.Explanation / Answer
Let us assume 1mol of water is present.
1mol of water = 18gm,
volume occupied by water = weight / density
Therefore volume of 1mol of ice = 18/ 0.917 = 19.63 ml
volume of 1mol of water liquid = 18 / 0.999 = 18.018 ml
We know 1 mol of water contains 6.023*1023 molecules
1molecule contains 2H atoms and 1 O atom,
=> 12.046*1023 H atoms and 6.023*1023 O atoms.
Volume of H atom = (4/3)* pi*r3 = (4/3)*3.1416*(37*10-10)3 = 2.1217*10-25 cm3
Volume of O atom = (4/3)*pi*(66*10-10)3 = 12.0426*10-25 cm3
Volume occupied byatoms = 12.046*1023* 2.1217*10-25 + 6.023*1023* 12.0426*10-25 = 0.98 cm3
For water, 1ml = 1c.c,
Volume occupied by atoms = 0.98 ml
Therefore %volume of free space in ice = (19.63-0.98)/19.63 = 95% free space
%volume of free space in liquid water = (18.018-0.98)/18.018 = 94.56% free space
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