When an airbag is inflated the nitrogen gas has a pressure of 1.30 atmospheres, a temperature of 301 K, and a volume of 40.0 liters. What is the volume of the nitrogen at STP?
1 Answer
Explanation:
You can actually use two approaches to solve this problem.
You can use the ideal gas law to find the number of moles of gas present in that sample, then use the known molar volume of a gas at STP conditions to find the new volume.
As a way to double-check the result you get by using this approach, you can use the combined gas law equation to find the new volume of the gas without finding out how many moles it contains.
So, the ideal gas law equation looks like this
#color(blue)(|bar(ul(color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "#
Here you have
#P# - the pressure of the gas
#V# - the volume it occupies
#n# - the number of moles of gas
#R# - the universal gas constant, usually given as#0.0821("atm" * "L")/("mol" * "K")#
#T# - the absolute temperature of the gas
Rearrange the equation to solve for
#PV = nRT implies n = (PV)/(RT)#
Plug in your values to find
#n = (1.30 color(red)(cancel(color(black)("atm"))) * 40.0 color(red)(cancel(color(black)("L"))))/(0.0821(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * 301color(red)(cancel(color(black)("K")))) = "2.104 moles N"_2#
Now, STP conditions are currently defined as a pressure of
In your case,
#2.104 color(red)(cancel(color(black)("moles N"_2))) * "22.7 L"/(1color(red)(cancel(color(black)("mole N"_2)))) = color(green)(|bar(ul(color(white)(a/a)color(black)("47.8 L")color(white)(a/a)|)))#
Now, you can double-check the result by suing the combined gas law
#color(blue)(|bar(ul(color(white)(a/a)(P_1V_1)/T_1 = (P_2V_2)/T_2color(white)(a/a)|)))#
Here
At mentioned before, STP conditions are defined as
#P_2 = "100 kPa" = 101/101.325color(white)(a)"atm"#
#T_2 = 0^@"C" + 273.15 = "273.15 K"#
Rearrange the combined gas law equation to solve for
#(P_1V_1)/T_1 = (P_2V_2)/T_2 implies V_2 = P_1/P_2 * T_2/T_1 * V_1#
Plug in your values to find
#V_2 = (1.30 color(red)(cancel(color(black)("atm"))))/(100/101.325color(red)(cancel(color(black)("atm")))) * (273.15color(red)(cancel(color(black)("K"))))/(301color(red)(cancel(color(black)("K")))) * "40.0 L"#
#V_2 = color(green)(|bar(ul(color(white)(a/a)color(black)("47.8 L")color(white)(a/a)|)))#
The answer is rounded to three sig figs.
SIDE NOTE STP conditions are often in accordance to their old definition of a pressure of
Under these conditions, one mole of any ideal gas occupies