How Does Adding Nitrogen Affect Pressure in a Sealed Vessel?

[frozen7]

A vessel of volume 0.2 m^3 contains nitrogen gas at 1.013 bar and 15 celsius. If 0.2 kg of nitrogen is now pumped into the vessel, calculate the new pressure when the vessel has returned to its initial temperature. The molecular weight of nitrogen is 28, and it may be assumed that the gas is a perfect gas. The universal gas constant is 8.314 kNm / kmoleK

I solve it in this way:

PV = nRT
P= nRT / V
= 200/28 x 8.314 x 288 x 1 / 0.2
= 85515 Pa
= 0.855bar

New pressure = 0.855bar + 1.013 bar
= 1.87 bar

The answer I get is same with the given correct answer. However, my lecturer told me that my solution is wrong even I got my final answer correctly. Can anyone explain to me what`s the reason?
Thanks in advance.

 

[vladb]

I can't see anything wrong with your solution. You're simply using Dalton's law here, which should be ok. Did your lecturer comment on where your mistake exactly was?

 

[Astronuc]

Perhaps the instructor is expecting one to calculate the intial number of moles of N₂ and then calculate the number of moles added, rather than using partial pressures.

 

[frozen7]

He told me that because I assume the temperature is constant. The way he solves the problem is by finding the total mass of the nitrogen gas at the final moment and count the pressure by using ideal gas law.

 

[frozen7]

Anyway, is my way to solve the problem correct?

 

[FredGarvin]

Your way is correct. It's actually a bit more to the point. Your instructor did the long way around which is just a different way to do it.

Just because it is not the same method as your instructor's doesn't mean it isn't correct. You didn't get marked down, did you? That wouldn't be right unless it was specified how the problem should be approached.