Ideal Gas Law Question

[FeralisExtremum]

I was doing some practice problems and came across this one:

In an 11.2 liter container the partial pressure of nitrogen gas is .5 atmospheres at 25 degrees C. What is the mass of nitrogen in the container?

So I used the ideal gas law formula (pv=nRT) to solve for the number of moles and then multiplied that by the molar mass of Nitrogen gas (28) and got ~6.4g. The problem is that was not an answer option, but 7g was. I checked the back for the solution and they basically used the combined gas law to say that if at STP 1 mole is 22.4L, then under these conditions we would have approximately .25 moles (1/2 as much volume and 1/2 as much pressure).

Why could I not just use the ideal gas law directly to solve this? Shouldn't plugging the numbers in give the same value, instead of having to compare it to STP conditions to get the answer?

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[KyoPhan]

I think your correct on this. The way they worked it out is assuming standard conditions. But it's not in standard condition because of the 25 degree celcius. They assume that the temp doesn't change the problem much, which is true because it is kind of off only by a little. However, if you want a more correct answer, you would use the pv=nRT.

Anyone else?

 

[J777]

I think that your answer is actually more accurate. They are approximating the answer. Since the numbers can be manipulated so that they match the standard volume of one mole of gas (half volume, temp is kinda close to 273, pressure is half of the stp pressure of 1 ATM), 7 would be a very rough estimate. Even so, this isn't a great assumption because using the standard volume of one mole of gas assume stp (273 K as the temp). However we have a temp of 298 in this problem so the answer would be smaller. If you plug 273 into pvnrt, and use the rest of the numbers provided and .08 for gas constant, you will get around 7

In short, your answer is better and would certainly be one of the options on the real thing