# How many atoms are in 131.97 liters of water vapor at STP?

Jun 3, 2017

Well the molar volume at $\text{STP}$, is $22.4 \cdot L \cdot m o {l}^{-} 1$. (Check this value out with your syllabus...........)

#### Explanation:

And so we take the quotient to get the number of moles.............

$\text{Number of moles} = \frac{131.97 \cdot L}{22.4 \cdot L \cdot m o {l}^{-} 1} = 5.8921 \cdot m o l$,

Note that this is dimensionally consistent as the $L$ cancels out, and $\frac{1}{m o {l}^{-} 1} = \frac{1}{\frac{1}{m o l}} = m o l$ as required.

Now we know that in ONE MOLE, there are $\text{Avogadro's Number}$ of particles, i.e. $6.0221 \times {10}^{23} \cdot m o {l}^{-} 1$

And thus.......................$\text{number of particles} = 6.0221 \times {10}^{23} \cdot m o {l}^{-} 1 \times 5.8921 \cdot m o l =$

$3.5479 \times {10}^{24}$ $\text{individual gas particles........}$

And since an individual gas particles CONTAINS THREE ATOMS, i.e. ${H}_{2} O \left(g\right)$, there are................

$3.5479 \times {10}^{24} \cdot {\text{molecules"xx3*"atoms"*"molecule}}^{-} 1$

$= 1.0644 \times {10}^{25} \cdot \text{atoms}$.

How many oxygen atoms, and how many hydrogen atoms?