Question

The last four digits of an ID number are 92.71 gal. Use that decimal number as a volume of water in gallons. (Ex. 10.33 gal). Show by dimensional analysis, without intermediate answers, the number of molecules in that volume of water.

Answer 1

Number of molecules in the given volume of water

= ( 92.71 gal) x ( 3.7854 L / 1gal) x ( 1000 ml / 1L) x ( 1g/ml) x ( 1 mol / 18 g) x ( 6.022 x 10^ 23 molecules / 1mol)

= 1.174 x 10^ 28 molecules

Answer 2

To determine the number of molecules in a given volume of water, we can use dimensional analysis and the concept of Avogadro's number.

Avogadro's number (Na) is defined as the number of atoms or molecules in one mole of a substance, which is approximately 6.022 × 10^23.

We can set up the dimensional analysis as follows:

(92.71 gal) x (6.022 × 10^23 molecules/mol) / (1 gal) = ? molecules

By multiplying the given volume (92.71 gal) by the conversion factor of (6.022 × 10^23 molecules/mol) divided by (1 gal), the gallons unit cancels out, leaving us with the number of molecules.

Performing the calculation, we get:

(92.71 gal) x (6.022 × 10^23 molecules/mol) / (1 gal) = 5.577 × 10^25 molecules

Therefore, the number of molecules in the given volume of water (92.71 gal) is approximately 5.577 × 10^25 molecules.