# Find out the molar fractions of all the involved gases

1. Nov 6, 2015

### TheSodesa

1. The problem statement, all variables and given/known data

5,00 moles of graphite and 5,00 moles of oxygen gas are stored in a metal bottle. The temperature is raised until the graphite starts burning. The burning produces a mixture of CO and CO2 gases in the vessel. After the temperature had returned to it's original value (after the reaction), the pressure inside the bottle had increased by 17%. Find out the molar fractions of each of the gases inside the bottle when all of the graphite is used up in the reaction.

Correct answers: xO2 = 0,145; xCO = 0,291; xCO2 = 0,564

2. Relevant equations

xi = pi/ptotal = ni/ntotal, where x = molar fraction.

Dalton's law: Sum(pi) = ptotal

pV = nRT

3. The attempt at a solution

I started out by forming the chemical equation:

3C + 2O2 -> 2CO + CO2

From this I calculated that nCO = (2/3)nC = 10/3 mol and nCO2 = (1/3)nC = 5/3 mol ( since we know that C is the limiting reactant). We can also see that the amount of used up oxygen is nO2 = nCO = 10/3 mol, so the amount oxygen gas remaining in the bottle after the reaction is nO2g = 5mol - nO2 = 5/3 mol, so the total amount of gas in the bottle (after the reaction) would be 20/3mol.

Next I assumed that the volume of C is negligible, so V is constant. T is also constant between the initial and final stages.This means that:

V0 = V1 <=> n0/p0 = n1/p1
= n1/1,17p0 (From pV = nRT).

=> n1gas = 1,17n0gas = 1,17 * 5 mol = 5,85 mol. However, the value of n1gas does not equal the total amount of moles I got from adding up the individual amounts of the different gases, and I'm not sure what to do next. I don't see how I could use Dalton's law to my advantage here, since i can't actually calculate the pressures because I know nothing about the temperature or the volume of the bottle.

Can anybody point me in the right direction? I am aware that I might not even need the actual values of the pressures or moles since I'm supposed to find the percentages, but I just don't know how to proceed.

2. Nov 6, 2015

### Staff: Mentor

There are 2 reactions occurring in parallel:

$C + O_2 ⇒ CO_2$
$C+\frac{1}{2}O_2⇒CO$

If x moles of C convert by the first reaction, then 5-x moles of C convert by the second reaction.

Chet

3. Nov 6, 2015

### TheSodesa

Alright, I'm going to try this after I'm done cooking (and eating) dinner. I'll report back when I'm done/if I get stuck again.

4. Nov 7, 2015

### TheSodesa

Alright, I'm back!
Turns out I was more tired than I though since I passed out in bed right after dinner so I couldn't get back to the problem before this morning. Anyways, your hint helped and I got the right answer, so thank you for that.

For future reference, should I always, always, always write separate chemical equations if I know that there are multiple reactions going on at the same time, even if they are drawing from the same pool of chemical(s) like C and O2 in this problem?

Last edited: Nov 7, 2015
5. Nov 7, 2015

### Staff: Mentor

I hate to answer "always" questions. Partly, it depends on the context of the problem statement. I would just use my judgement on the specific problem.

6. Nov 7, 2015

### TheSodesa

Got it. Thanks for the help.