Question #48160
1 Answer
Explanation:
The idea here is that you need to use the ideal gas law equation and the molar mass of nitrogen gas,
Now, STP conditions will most likely be given to you as a pressure of
The ideal gas law equation looks like this
#color(blue)(|bar(ul(color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "# , where
As you know, a compound's molar mass tells you the mass of one mole of that substance. IN your case, nitrogen gas has a molar mass of
#M_M = "28.0134 g mol"^(-1)#
This means that every mole of nitrogen gas has a mass of
You can thus replace the number of moleso f nitrogen gas,
#n = m/M_M#
Plug this into the ideal gas law equation to get
#PV = m/M_M * RT#
Rearrange to get
#PV *M_M = m * RT#
This will be equivalent to
#P * M_M = m/V * RT#
But since density,
#m/V = (P * M_M)/(RT)#
and therefore
#color(purple)(|bar(ul(color(white)(a/a)color(black)(rho = (P * M_M)/(RT))color(white)(a/a)|)))#
Now all you have to do is use the STP values for pressure and temperature and the molar mass of nitrogen gas to get
#rho = (1 color(red)(cancel(color(black)("atm"))) * "28.0134 g" color(red)(cancel(color(black)("mol"^(-1)))))/(0.0821(color(red)(cancel(color(black)("atm"))) * "L")/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * 273,15color(red)(cancel(color(black)("K")))) = color(green)(|bar(ul(color(white)(a/a)"1.25 g L"^(-1)color(white)(a/a)|)))#
ALTERNATIVE APPROACH
As you know, one mole of any ideal gas kept at
Moreover, you know that one mole of nitrogen gas has a mass of
#1 color(red)(cancel(color(black)("L N"_2))) * overbrace((1 color(red)(cancel(color(black)("mole N"_2))))/(22.4color(red)(cancel(color(black)("L N"_2)))))^(color(purple)("molar volume of a gas at STP")) * overbrace("28.0134 g"/(1color(red)(cancel(color(black)("mole N"_2)))))^(color(blue)("molar mass of N"_2)) = "1.25 g"#
Since this is how many grams you get per liter of nitrogen gas at STP, it follows that its density will be
#rho = color(green)(|bar(ul(color(white)(a/a)"1.25 g L"^(-1)color(white)(a/a)|)))#