[Borek]

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?

[DrCMS]

No

[curiouscat]

No

Agreed.

[Borek]

While I agree with the answer, anyone cares to explain?

[curiouscat]

While I agree with the answer, anyone cares to explain?

$$n=\frac{PV}{RT} \\ n_{CH_4} = n_{O_2} = n_{mix}=n \\ n M_{CH_4} + m_{flask}=67 \\ n M_{O_2}  + m_{flask}=69 \\ n=\frac{1}{8} \\ m_{flask}=65 \\ 67.5-65= \left ( x_{CH_4} M_{CH_4} + (1-x_{CH_4}) M_{O_2} \right ) \times \frac{1}{8} \\ x_{CH_4}=\frac{3}{4} \\ x_{O_2}=\frac{1}{4} \\ $$

[DrCMS]

Doing the maths another way the flask plus methane and oxygen would need to weigh at least 68.34g for complete combustion.

[curiouscat]

Doing the maths another way the flask plus methane and oxygen would need to weigh at least 68.34g for complete combustion.

Glad. I get the same.

[curiouscat]

BTW, was the fact that P and T were constant supposed to be obvious somehow? Or implied?

[Borek]

Implied.

[DrCMS]

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.