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General : Determining the number of liters of SO3(g) produced from the combustion of coal
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 Message 1 of 6 in Discussion 
From: MSN Nicknamenavyovermyhead  (Original Message)Sent: 1/8/2006 8:04 PM
Since I believe I figured out my problem with the earth's ozone question let me lay this one on you.

How do I figure the number of liters of SO3(g) produced at 25 degrees celcius and 1.00 atm from the combustion of 1.00 kg coal which is 1.00% S by weight? The assumption is that all the sulfur in the coal ends up as SO3.

I don't even know where to begin with this one.


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 Message 2 of 6 in Discussion 
From: MSN Nickname·Steve·Sent: 1/9/2006 4:49 AM
This is a stoichiometry problem in which you calculate the amount of SO3 in units of liters at a certain temperature and pressure that are formed from the combustion of a certain amount of sulfur, which you will have to calculate.  Overall, you will be following the "fabulous four steps" for stoichiometry problems:
 
 
Step 1:  Write the balanced chemical equation for the reaction.
 
Step 2:  Calculate the moles of "given" substance, (if more than one reactant amount is given, calculate the moles of each and determine which is the limiting reactant).
 
Step 3:  Calculate the moles of "desired" substance from your answer in step 2 using the coefficients from the balanced chemical equation.
 
Step 4:  Convert your answer in step 3 to the units the problem asks for.  Usually this is grams, but it could be volume (for gases) or concentration (such as molarity, for solutions).
 
 
 
 
Step 1.  The balanced chemical equation for the combustion of sulfur to sulfur trioxide is
 
S8 (s)  +  12 O2 (g)      8 SO3 (g)
 
Here I used the actual molecular formula for yellow sulfur which is S8, but we would get the same final answer if we just used "S (s)" instead, as some textbooks do.
 
 
Step 2 is to calculate the moles of "given" substance in the reaction, which is sulfur, S8.  Take one percent of 1 kg, since that is the amount of sulfur in the one kg of coal, convert to grams, and then to moles using the molecular weight of S8.
 
 
Step 3 is where you use the coefficients in the balanced chemical equation to calculate the moles of "desired" substance, the SO3.  It's just like a conversion problem starting with the moles of S8 you calculated in Step 2:
 
XXX mol S8   X   8 mol SO3    =    YYY mol of SO3
       1                1 mol S8
 
See how the moles of S8 cancel, leaving you with moles of SO3 in the answer. 
 
 
Step 4 will be to convert the moles of SO3 gas you calculated in Step 3 ("YYY") to liters, which you can do using the ideal gas law:
 
PV  =  nRT,    V  =  nRT / P
 
 
And that will do it!
 
 
Steve

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 Message 3 of 6 in Discussion 
From: MSN NicknamenavyovermyheadSent: 1/10/2006 1:30 AM
Okay, so let me see if I got this right.  1kg is the same as 1000g, so 1% of 1000g is 10g.  The molecular mass of S8 = 32.065 x 8 = 256.520 amu.  Molar mass of S8 = 256.52 g/mol.
 
10g/256.52 g/mol = .0389833
 
.0389833 mol S8/1  x  8 mol SO3/1 mol S8 = .311866 mol of SO3
 
V = nRT/P
V = (.311866)(.08206)(298)/1.00
V = 7.62633 L
 
Does that about do it?
 
Marc

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 Message 4 of 6 in Discussion 
From: MSN Nickname·Steve·Sent: 1/10/2006 4:18 AM
Looks good to me! 
 
To three significant figures, the answer is 7.63 L.  (I always use extra significant figures whenever possible (e.g., in atomic weights and in constants like R, as you did here also) and finally round the final answer according to the given measured value that has the fewest significant digits - this is the rule for multiplication and division which is mostly what we are doing in these calculations.)
 
 
Steve

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 Message 5 of 6 in Discussion 
From: MSN NicknamenavyovermyheadSent: 1/10/2006 12:04 PM
Thanks, I think I punched numbers in the calculator 20 times to finally get my answer.  I'm sure I'll be asking you for more help in the NEAR future.
 
Marc

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 Message 6 of 6 in Discussion 
From: MSN Nickname·Steve·Sent: 1/10/2006 9:00 PM
OK Marc, you bet!
 
>>  I think I punched numbers in the calculator 20 times to finally get my answer  <<
 
I remember doing that a lot with physics!
 
 
Steve

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