# A cylindrical glass of water ( H 2 O ) has a radius of 6.12 cm and a height of 9.91 cm. The...

## Question:

A cylindrical glass of water ({eq}H_2O {/eq}) has a radius of 6.12 cm and a height of 9.91 cm. The density of water is 1.00 g/cm{eq}^3 {/eq}. How many moles of water are contained in the glass?

## Molar Mass.

It is defined as the mass of a substance divided by its number of moles. It is generally expressed as grams per mole. On the other hand, density is a physical dimension expressed as units of mass divided by units of volume.

{eq}\text{Known data:}\\ H_2\,O\\ r = 6.12\,cm\\ h = 9.91\,cm\\ \rho = 1.00\,g/cm^3\\ M = 18.0\,g/mol\\ n = ?\\ {/eq}

We are going to determine the mass of water from the definition of density.

{eq}m = \rho \,V \\ {V_{{\text{cylinder}}}} = \pi \,{r^2}h \\ m = \rho \,\pi \,{r^2}h \\ {/eq}

The number of moles of a substance is equal to the mass divided by molecular mass.

{eq}n = \dfrac{m}{M} = \dfrac{{\rho \,\pi \,{r^2}h}}{M}\\ {/eq}

Replacing known data:

{eq}n = \dfrac{{\left( {1.00\,g/c{m^3}} \right)\,\pi \left( {6.12\,cm} \right){\,^2}\left( {9.91\,cm} \right)}}{{18.0\,g/mol}} = 64.8\,moles\\ {/eq}

There's 64.8 moles of water in the glass.