# How can I find the volume of 3.0 x 10(25) molecules of Neon gas at STP?

Dec 10, 2014

The answer is $1100 L$.

In order to determine the volume of $N e$ gas at STP, you need to know that at STP (standard temperature and pressure), $1$ mole of any ideal gas occupies exactly $22.4 L$.

We must however find out how many moles of $N e$ we are dealing with. We do this by using Avogadro's number - $6.022 \cdot {10}^{23}$ -, which tells us how many molecules are in $1$ mole of a substance.

$\left(3.0 \cdot {10}^{25} m o l e c u l e s\right) \cdot \frac{1 m o l e}{6.022 \cdot {10}^{23} m o l e c u l e s} = 49.8$

moles; this means that $3.0 \cdot {10}^{25}$ molecules make up $49.8$ moles of $N e$ gas.

We can now find out the volume by using

${n}_{N e} = \frac{V}{V} _ \left(m o l a r\right) \to V = {n}_{N e} \cdot {V}_{m o l a r}$

$V = 49.8 m o l e s \cdot 22.4 \frac{L}{m o l e} = 1100 L$ -> rounded to two sig figs.

Dec 10, 2014

You can determine the volume of $\text{3.0 x 10"^25}$ molecules of Neon at STP using the ideal gas law: $\text{PV}$ = $\text{nRT}$, solving for V. You must convert the molecules of Neon to moles using Avagadro's number, ${\text{6.022 x 10}}^{23}$. STP for gas laws is $\text{0"^"o""C}$ and 1 atm. You will need to convert the Celsius temperature to Kelvins, which is the temperature scale used in the gas laws.

Convert molecules of Neon to moles.

${\text{3.0 x 10}}^{25}$ $\text{molecules Ne}$ x $\text{1 mol Ne}$$/$$\text{6.022 x 10"^23 "molecules Ne}$ = $\text{49.82 moles Ne}$
(I'm leaving some guard units to reduce rounding errors.)

Given/Known:
P = 1 atm
n = 49.82 moles
R = ${\text{0.08205746 L atm K"^(-1) "mol}}^{- 1}$
T = $\text{0"^"o""C" + "273.15" = "273.15K}$

Unknown:
Volume

Equation:
$\text{PV}$ = $\text{nRT}$

Solution:
Divide both sides of the equation by P. Solve for V.

$\text{V}$ = $\text{nRT"/"P}$
$\text{V}$ = $\text{49.82 moles x 0.08205746 L atm K"^(-1) "mol"^(-1)}$ x $\text{273.15K/1 atm}$ = $\text{1100 L}$
(The answer is rounded to two significant figures because ${\text{3.0 x 10}}^{25}$ has two significant figures.)

The volume of ${\text{3.0 x 10}}^{25}$ $\text{molecules Ne}$ at STP is $\text{1100 L}$.