Stoichiometry of Gaseous Reactions

**The Question:**


*How many liters of $H\_2S$ would be required to react with excess oxygen to produce $12.0$ $L$ of $SO\_2$? The reaction yield is $88.5$%. Assume constant temperature and pressure throughout the reaction.*


**My Approach:**


I used dimensional analysis to convert from liters of $SO\_2$ to $moles$ of $H\_2S$ and then used Avogadro`s Law ($\frac{V\_1}{n\_1} = \frac{V\_2}{n\_2}$) to find the volume of $H\_2S$ in liters.


**Dimensional Analysis:**
$\frac{1}{.885} \* \frac{12.0L}{1} \* \frac{1 g}{1 mL} \* \frac{1 mol SO\_2}{64g} \* \frac{2 mol SO\_2}{2 mol H\_2S} \* \frac{1 mol H\_2S}{34 g} = 6.23$ $mol$ $of$ $H\_2S$.


**Avogadro`s Law:**
$\frac{12.0L}{166 mol} \* \frac{ L }{6.23 mol}$


End Result = $.028 L$


^ The end result does not seem right and any help in remedying my approach or shedding light on another approach would be much appreciated. Thanks in advance!




I never really learned the method of solving this stuff with Avogadro's Law, but here's an almost identical way.


Your balanced equation is as follows...


$\ce{2H2S + 3O2 -> 2SO2 + 2H2O}$, and I think you agree on that by looking at your calculations.


At a given temperature and pressure, $1 mol = x L$. For example, at STP (standard temperature and pressure) this is $1 mol = 22.4 L$. It wasn't exactly defined what temperature and pressure are, but they are constant, so we can use a variable $x$ to denote some conversion (which cancels out anyway, I assume giving rise to Avogadro's Law).


$12.0L\_{\ce{SO2}} \* \frac{1mol\_{\ce{SO2}}}{xL\_{\ce{SO2}}} \* \frac{2mol\_{\ce{H2S}}}{2mol\_{\ce{SO2}}} \* \frac{xL\_{\ce{H2S}}}{1mol\_{\ce{H2S}}} = 12.0L\_{\ce{H2S}}$


But this is assuming $100\%$ yield. I see you divided by $0.885$ above, which is correct, but I've gotten a metric ton of these wrong before, so I prefer the proportions way.


Regardless, $\frac{12L\_{\ce{H2S}}}{0.885} = 13.6L\_{\ce{H2S}}$


I think you definitely overcomplicated things by assuming a density of $1g/mL$ among other things. Your dimensional analysis also seems strange near the end of the left hand side where you somehow cancel $g$ with $mol\_{\ce{SO2}}$.


If I were to do it with Avogadro's Law (taking a guess here), I'd still get $12.0L$ because the mole ratio is the same. And then I'd divide like you did.


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