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### Topic: Problem of the week - 07/01/2013  (Read 17311 times)

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#### Borek

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##### Problem of the week - 07/01/2013
« on: January 07, 2013, 11:26:48 AM »
A flask filled with a mixture of oxygen and methane weights 67.5 g. The same flask filled with methane weights 67.0 g, and filled with oxygen - 69.0 g.

Is there enough oxygen for a complete combustion of the methane in the mixture?
« Last Edit: January 07, 2013, 11:58:48 AM by Borek »
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#### DrCMS

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##### Re: Problem of the week - 07/01/2013
« Reply #1 on: January 07, 2013, 02:47:57 PM »
No

#### curiouscat

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##### Re: Problem of the week - 07/01/2013
« Reply #2 on: January 09, 2013, 04:47:12 AM »

#### Borek

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##### Re: Problem of the week - 07/01/2013
« Reply #3 on: January 10, 2013, 05:32:07 AM »
While I agree with the answer, anyone cares to explain?
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#### curiouscat

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##### Re: Problem of the week - 07/01/2013
« Reply #4 on: January 10, 2013, 07:18:51 AM »
While I agree with the answer, anyone cares to explain?

$$n=\frac{PV}{RT} \\ n_{CH_4} = n_{O_2} = n_{mix}=n \\ n M_{CH_4} + m_{flask}=67 \\ n M_{O_2} + m_{flask}=69 \\ n=\frac{1}{8} \\ m_{flask}=65 \\ 67.5-65= \left ( x_{CH_4} M_{CH_4} + (1-x_{CH_4}) M_{O_2} \right ) \times \frac{1}{8} \\ x_{CH_4}=\frac{3}{4} \\ x_{O_2}=\frac{1}{4} \\$$
« Last Edit: January 10, 2013, 08:11:03 AM by curiouscat »

#### DrCMS

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##### Re: Problem of the week - 07/01/2013
« Reply #5 on: January 10, 2013, 07:46:54 AM »
Doing the maths another way the flask plus methane and oxygen would need to weigh at least 68.34g for complete combustion.

#### curiouscat

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##### Re: Problem of the week - 07/01/2013
« Reply #6 on: January 10, 2013, 08:04:03 AM »
Doing the maths another way the flask plus methane and oxygen would need to weigh at least 68.34g for complete combustion.

#### curiouscat

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##### Re: Problem of the week - 07/01/2013
« Reply #7 on: January 10, 2013, 08:50:05 AM »
BTW, was the fact that P and T were constant supposed to be obvious somehow? Or implied?

#### Borek

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##### Re: Problem of the week - 07/01/2013
« Reply #8 on: January 10, 2013, 10:46:14 AM »
Implied.
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#### DrCMS

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##### Re: Problem of the week - 07/01/2013
« Reply #9 on: January 10, 2013, 11:22:40 AM »
Yes usually if Borek is being sneaky you can see it in the question.  As this one was quite simply worded the only way to solve it was to assume P and T were unchanged for each.