How small is a water molecule compared to the volume of liquid water?

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In summary, one mole of liquid water has a volume of 18 cm3 and each molecule is at the center of a small cube. To find the length of the sides, the volume per molecule must be determined by knowing the number of molecules in a mole. This can then be compared to the diameter of a molecule.
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One mole of liquid water occupies a volume of 18 cm3. Imagine that each molecule on the average is at the centre of a small cube. (i) What is the length of the sides of this small cube? (ii) Compare this length with the diameter of a molecule.
 
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1 gram-mole of water has a mass of approximately 18 g, and since water has a density of approximately 1 g/cm3, it has a volume of cm3. How many molecules are in a mole? Knowing that, one can detemine the volume per molecule. One should be able to find the side length from the volume of a cube.
 
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(i) To find the length of the sides of the small cube, we can use the formula for volume of a cube, V = s^3, where s is the length of the sides. Plugging in the given volume of 18 cm^3, we get 18 = s^3. Solving for s, we get s = 2.6 cm. Therefore, the length of the sides of the small cube is 2.6 cm.

(ii) The diameter of a water molecule is approximately 0.28 nanometers (nm). Converting this to centimeters, we get 0.000000028 cm. Comparing this with the length of the sides of the small cube, we can see that the cube is much larger than the diameter of a water molecule. In fact, the cube is approximately 93 million times larger than the diameter of a molecule. This shows how small individual molecules are compared to the macroscopic world that we are able to see and interact with.
 

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