This question deals with the concept of the mole. A mole is a nickname for Avogadro's number, 6.02 x 1023 . It is one of the most useful tools in science because it allows conversion of a compound or element's mass into a count of how many molecules/atoms are present in that sample.
For example, carbon, C, has an atomic mass of 12.0 amu (atomic mass units), a number that can be found on all periodic tables. It is an amazingly useful fact that the atomic mass of each element is also what is called it's "molar mass. Carbon has a molar mass of 12.0 g/mole. Each 12.0 grams of carbon contain one mole, or 6.02 x 1023, of carbon atoms. Oxygen's atomic weight is 16.0 amu and hydrogen is 1.0 amu. In both cases, these may be written as 16.0 g/mole and 1.0 grams/mole. If you have 1.0 grams of H atoms, you have one mole of H atoms. [Be aware that both oxygen and hydrogen are diatomic in normal conditions, so the gases O2 and H2 are the natural forms for these elements. The molar masses of the molecular forms are thus 32.0 g/mole and 2.0 g/mole].
To answer the question of how many molecules of H2O there are in 25.00 grams of water, pay close attention to the units. We need to molar mass of H2O, which we find by adding the atomic masses of all the elements, including the number of times they appear. For H2O we have:
2 H at 1.0 each = 2.0 amu
1 O at 16.0 each = 16.0 amu
Total for H2O = 18.0 amu, or grams/mole
It takes 18 grams of H2O to obtain 1 mole, or 6.02 x 1023 molecules of water. Think about that before we answer the question. We have 25.0 grams of water, so we have more than one mole of water molecules. To find the exact number, divide the available mass (25.0g) by the molar mass (18.0g/mole). Watch how the units work out. The grams cancel and moles moves to the top, leaving moles of water. [g/(g/mole) = moles].
Here we have 25.0 g/(18.0g/mole) = 1.39 moles water (3 sig figs).
Multiply 1.39 moles times the definition of a mole to arrive at the actual number of water molecules:
1.39 (moles water) * 6.02 x 1023 molecules water/(mole water) = 8.36 x 1023 molecules water.
That's slightly above Avogadro's number, which is what we expected. Keeping the units in the calculations is annoying, I know, but it helps guide the operations and if you wind up with the unit desired, there is a good chance you've done the problem correctly.
Explanation:
