(a) Find the approximate number of water molecules in 1.00 L of water. (b) What fraction of the

(a) Find the approximate number of water molecules in 1.00...

Key Concepts

Mole Concept and Avogadro's Number

This concept involves the use of Avogadro's number, which is approximately 6.02 x 10^23 particles per mole, to relate the mass of a substance to the number of its constituent molecules. It is essential for converting the mass (derived from volume and density) into the number of water molecules in a given volume.

Density and Molar Mass

The density of water (nearly 1 g/mL) combined with its molar mass (about 18.02 g/mol) allows us to convert a given volume of water into its corresponding mass and then into moles. This conversion is vital in determining the total number of water molecules in a liter of water.

Nuclear Size and Volume Estimation

In nuclear physics, the volume of a nucleus is typically estimated using the formula for a sphere, V = (4/3)?R^3, where the radius R is approximated by relationships such as R ? 1.2 fm × A^(1/3) (with A being the mass number). This estimation is crucial for understanding how small the nucleus is compared to the overall atomic or molecular volume.

Volume Fraction Calculation

This concept relates to determining the ratio of the total volume occupied by the water nuclei to the overall volume of the water sample. It involves comparing the minute volume of each nucleus to the much larger volume of the entire molecule or substance, offering insight into the negligible volume fraction that the dense nuclei occupy.

Transcript

00:01 To find the number of water molecules, we know that 1 meter of water is actually 1 .00 kilograms.

00:12 Okay, now we want to find the mass of each water molecule.

00:19 Take 2 times the mass of hydrogen plus mass of oxygen.

00:26 We can find the atomic mass units for these nuclei.

00:36 For this for hydrogen and then for oxygen it's this multiply that by the conversion factor that converts from atomic mass units to kilograms we have the mass of each mass of each molecule to be as such now to find a number of molecules we simply take the total mass which is one kilogram divide by 2 .9914, 26, should get 3 .34 times 10 to power 25 molecules.

01:32 For the next part, we want to calculate what is the fraction of the volume of water that's occupied by the nucleus.

01:42 Alright, and we first find the total, what is the total volume of the water.

01:52 Total volume of water is actually one liters and one liter converting it into meter cube is actually 10th of power of manistri meter cube now we want to use the approximation for a radius of a nuclei radius of a nuclei is r naught multiplied by the nuclear number to the power 1 3rd.

02:30 Alright.

02:31 And we are approximating that the nucleus are all spheres, right, perfect spheres.

02:37 And so the volume of the spheres are actually 4 3rd pi are q.

02:46 So now for a water molecule we have 3 spheres, right? two of them are the hydrogen.

02:53 So we have the 2 times of the hydrogen r of h plus r of the oxygen.

03:07 Let me just differentiate it from aranot, right? so r0 over here is a constant, it's a 1 .2 times 7 .7 p .m...

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