Question

How many moles are 2.54 x 10^29 molecues of H2O

Answer 1

`\boxed {\boxed {\sf 421,786.7818 \ mol \ H_2O}}`

Step-by-step explanation:

We are asked to convert from molecules of water to moles.

1. Avogadro's Number

1 mole of any substance contains the same number of particles (atoms, molecules, formula units, etc). This is Avogadro's Number: 6.022*10²³. In this problem, the particles are molecules of water.

2. Convert Molecules to Moles

Use Avogadro's Number to make a ratio.

`\frac {6.022 *10^(23) \ molecules \ H_2O}{1 \ mol \ H_2O}`

Multiply by the number of molecules given: 2.54 *10²⁹

`2.54 *10^(29) \ molecules \ H_2O * \frac {6.022 *10^(23) \ molecules \ H_2O}{1 \ mol \ H_2O}`

Flip the ratio so the units of molecules of water cancel.

`2.54 *10^(29) \ molecules \ H_2O * \frac {1 \ mol \ H_2O}{6.022 *10^(23) \ molecules \ H_2O}`

`2.54 *10^(29) * \frac {1 \ mol \ H_2O}{6.022 *10^(23) }`

Condense the problem into 1 fraction.

`\frac {2.54 *10^(29) }{6.022 *10^(23) }\ mol \ H_2O`

`421786.7818 \ mol \ H_2O`

2.54 *10²⁹ molecules of water are 421, 786.7818 moles of water.