Question

practice: mole-particle & particle-mole
a cup of water contains 13.9 moles of water. how many molecules of water are in the cup?
image of a conversion factor setup with boxes to fill
options: 1 mole, 6.02×10²³ molecules of h₂o, 13.9 moles h₂o, 2.31×10²³ molecules h₂o, 4.33×10² molecules h₂o, 8.37×10²⁴ molecules h₂o

Explanation:

Step1: Identify the given and conversion factor

We know the number of moles of water is \(13.9\) moles, and the conversion factor between moles and molecules is Avogadro's number, which is \(6.02\times 10^{23}\) molecules per mole.

Step2: Set up the calculation

To find the number of molecules, we multiply the number of moles by Avogadro's number. So the formula is: \(\text{Number of molecules}=\text{Moles}\times\text{Avogadro's number}\)
Substituting the values: \(13.9\space\text{moles}\times6.02\times 10^{23}\space\frac{\text{molecules}}{\text{mole}}\)

Step3: Perform the multiplication

\(13.9\times6.02\times 10^{23}=(13.9\times6.02)\times 10^{23}\)
\(13.9\times6.02 = 83.678\)
So, \(83.678\times 10^{23}=8.3678\times 10^{24}\approx8.37\times 10^{24}\) molecules of \(H_2O\)

Answer:

The number of water molecules in the cup is \(\boldsymbol{8.37\times 10^{24}}\) molecules of \(H_2O\)