please i need help with this chemistry problem?

Question

two flasks are connected with a stopcock. the first flask has a volume of 5 liters and contains nitrogen gas at a pressure of .75 atm. the second flask has a volume of 8L and contains oxygen gas at a pressure of .125 atm. when the stopcocl between the flasks is opened and the gases are free to mix what will the pressure be in the resulting mixture?

Answer 1

Doing it the "hard way"

PV=nRT solve for moles n = PV/RT
plug in the values given:

0.75atm x 5li/0.08206latm/mol K x 273K = 0.167mol

0.125atm x 8li/0.8206latm/mol K x 273K = 0.446mol

Now total your moles and re-plug into gas law solving for pressure, remember, volume is now 13liters!:

0.167 + 0.446 = 0.212mol

P = nRT/V = [0.212mol x 0.8206latm/mol K x 273 ]/13liter

= 0.365 atm.

Now, the easy way:

[5/13 x 0.75atm] + [8/13 x 0.125atm] = 0.366atm

There is a slight difference between the 2 methods; I'm not certian if it is an inaccuracy, or rounding effects.