Question

A plastic bin is found to hold 3.1x10^24 molecules of water.

Calculate the number of moles in the container.

Answer 1

`\boxed {\boxed {\sf 5.1 \ mol \ H_2O}}`

Step-by-step explanation:

To convert from representative particles to moles, Avogadro's Number: 6.02*10²³, which tells us the number of particles (atoms, molecules, etc.) in 1 mole of a substance.

We can use it in a ratio.

`\frac {6.02*10^(23) \ molecules \ H_2O}{1 \ mol \ H_2O}`

Multiply by the given number of molecules.

`3.1*10^(24) \ molecules \ H_2O*\frac {6.02*10^(23) \ molecules \ H_2O}{1 \ mol \ H_2O}`

Flip the ratio so the molecules of water cancel out.

`3.1*10^(24) \ molecules \ H_2O*\frac {1 \ mol \ H_2O}{6.02*10^(23) \ molecules \ H_2O}`

`3.1*10^(24) *\frac {1 \ mol \ H_2O}{6.02*10^(23) }`

`\frac {3.1*10^(24) \ mol \ H_2O}{6.02*10^(23) }`

Divide.

`5.14950166113 \ mol \ H_2O`

The original number of molecules has 2 significant figures: 3 and 1, so our answer must have the same. For the number we calculated, that is the tenth place. The 4 in the hundredth place tells us to leave the 1.

`5.1 \ mol \ H_2O`

There are about 5.1 moles of water in 3.1*10²⁴ molecules of water.