# How many molecules in a given volume of fluid?

Oct 23, 2017

Well, for liquids you need to be quoted density, $\rho$....

#### Explanation:

And for gases you need pressure, volume, and temperature......

So let us take an example.....$\text{how many molecules of water are in 1 mL of water?}$

We know that ${\rho}_{\text{water}} = 1 \cdot g \cdot m {L}^{-} 1$

And to find the number of molecules we need the molar quantity....

"Mass"/"Molar mass"xxN_A=(rho_"water"xx"volume")/(18.01*g*mol^-1)xxN_A

...where ${N}_{A} \equiv \text{Avocado number} = 6.022 \times {10}^{23} \cdot m o {l}^{-} 1$...

And thus....

$\frac{1 \cdot g \cdot m {L}^{-} 1 \times 1 \cdot m L}{18.01 \cdot g \cdot m o {l}^{-} 1} \times 6.022 \times {10}^{23} \cdot m o {l}^{-} 1 = 3.34 \times {10}^{22}$ And note this is indeed a dimensionless number, as required....

For gases, as well, you know the Ideal Gas equations, and these can be manipulated to give the answer in moles, which represent the number of gaseous particles, of molecules.

And thus here we use $\text{the mole}$ as a collective number, precisely as we would use $\text{a dozen}$, or $\text{a score}$, or $\text{a gross}$. Except here the $\text{1 mole"=6.022xx10^23*"individual particles}$.

You happy with this? Because this is a fundamental concept to incorporate in your understanding.