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The Question that I wrote:

C4H10 (g) + O2 (g) --> CO2 (g) + H2O (g) [unbalanced]

Two closed, rigid vessels are connected by a stopcock. One vessel contains C4H10 with a pressure of 2.34  atm. The other vessel contains O2 with a pressure of 2.96 atm. The experiment is carried out at constant temperature when the stopcock is opened. What is the partial pressure (in Pa) of CO2 when the partial pressure of C4H10 decreases to 0.86 atm?

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My attempt:

C4H10 (g) + 13/2 O2 (g) --> 4 CO2 (g) + 5 H2O (g)

So, since everything else is constant during the chemical reaction, the moles ratios can be expressed as pressure ratios. Whatever happens to one side of the equation will happen to the other side as well.

C4H10 (g) + 13/2 O2 (g) --> 4 CO2 (g) + 5 H2O (g)
2.34 atm + 2.96 atm --> 0 atm + 0 atm   before
0.86 atm                  --> x atm      after
1.48 atm         =   1.48 atm      change

x = 1.48 atm

I can convert it easily to Pa, but the question is: Do I need to worry about the coefficients of an equation? (ex: Would I need to multiple the pressure by 4?) Did I even do this right? Thanks in advance!

Curious as to why you didn't balance it like this

2C4H10 + 13O2 → 8CO2 + 10H2O

Well, think about it. The coefficients are the ratios of the moles (or liters or pressure, etc.), right? And, what we are comparing in this problem is the C4H10 and CO2. The ratio of them in your version of the balanced equation (which is not wrong) is 2:8, respectively. This can be simplified to 1:4, right? My version of the equation just includes the simplest ratio of
C4H10 : CO2.

Anyone else want to offer some feedback? Come on. Don't be shy. :)

I totally agree with you, I was just curious as to why you didn't use whole numbers. It doesn't make sense to me if someone were to say, for example, half a molecule of whatever. I've always learnt to use whole numbers as the coefficients.