Am i overcomplicating things?

[DB]

Gas laws problem

2.44e23 molecules of Hydrogen and 3.0 molecules of Nitrogen are together exerting a pressure of 620. kPa. what is the partial pressure of each gas?
Ans_2 = 278 kPa, N_2 = 342 kPa

so basically the way i though of solving this was to use the ideal gas law being:

$$PV=nRT$$

i kept the temperature constant at 273 K. then i found the total amount of moles by adding the # of molecules and dividing by 6.02e23:

$$\frac{2.44e23+3.0e23}{6.02e23}=\sim 0.90 mol$$

so then i asked myself: at constant temperature, what would be the total volume these gases would occupy at 620 kPa and 0.90 mol. so i solved:

$$620x=0.90*8.31*273$$

$$x\sim 3.29_L$$

so now i took hydrogen, at constant temperature, occuping a volume of 3.29 L, how much pressure would it exert? 2.44e23 is 0.41 mol so..

$$3.29x=0.41*8.31*273$$

$$x\sim 282.7_{kPa}$$

so now by law of partial pressures 620-282.7=337.3 kPa
so my answer is:

$$H_2 = 282.7_{kPa}$$

$$N_2 = 337.3_{kPa}$$

i got it wrong, i think I am overcomplicating things, could some1 help me out?

thnx

 

[Umabel]

You didn't got it wrong. There is some round off error, because you did it the "long" way.

Try to look it over again and see if you can find an easier way. If you can't see it, let us know and we'll help out.

 

[DB]

i knew i was doing too much, before i posted it i had been looking and looking for an easier way n i really feel like I am missing it, some help would be great.

 

[DB]

just a reminder
i have a test monday so some help would be greatly apreciated

 

[Physics Monkey]

The simple way to find the partial pressure of each component is to multiply the total pressure by the mole fraction. Thus $$n = n_1 + n2$$ and so $$P_1 = \frac{n_1}{n} P$$ and $$P_2 = \frac{n_2}{n} P$$. This formula can be derived using the ideal gas law applied to the gas of $$n_1$$, the gas of $$n_2$$, and finally the gas of $$n_1 + n_2$$. Each of these applications is valid because no one "sees" anyone else, everybody is ideal.

$$P_1 V = n_1 R T$$

$$P_2 V = n_2 R T$$

$$P V = (n_1 + n_2) R T$$

 

[DB]

thanks man, i see it