The volume of a bicycle tire is 1.35 liters and the manufacturer recommends a tire pressure of 8.5 atm. If you want the bicycle tire to have the correct pressure at 20.0°C, what volume of air is required at STP?

1 Answer
Mar 5, 2016

Answer:

#"11 L"#

Explanation:

The idea here is that you need to figure out what volume of gas held at STP conditions is needed in order for the tire to have a volume of #"1.35 L"# at #"8.5 atm"# and #20.0^@"C"#.

Since pressure, temperature, and volume change, you can use the combined gas law equation to find the volume of gas at STP.

The combined gas law equation looks like this

#color(blue)(|bar(ul((P_1V_1)/T_1 = (P_2V_2)/T_2))|)" "#, where

#P_1#, #V_1#, #T_1# - the pressure, volume, and absolute temperature of the gas at an initial state
#P_2#, #V_2#, #T_2# - the pressure, volume, and absolute temperature of a gas at a final state

So, STP conditions are defined as a pressure of #"100 kPa"# and a temperature of #0^@"C"#. To convert the pressure to atm and the temperature to Kelvin, use the conversion factors

#"1 atm " = " 101.325 kPa"#

#T["K"] = t[""^@"C"] + 273.15#

You're starting with the gas under STP conditions, then changing its temperature to #20.0^@"C"# and its pressure to #"8.5 atm"#.

Rearrange the combined gas law equation to solve for #V_1#

#(P_1V_1)/T_1 = (P_2V_2)/T_2 implies V_1 = P_2/P_1 * T_1/T_2 * V_2#

Plug in your values to get

#V_1 = (8.5 color(red)(cancel(color(black)("atm"))))/(100/101.325color(red)(cancel(color(black)("atm")))) * ((273.15 + 0)color(red)(cancel(color(black)("K"))))/((273.15 + 20.0)color(red)(cancel(color(black)("K")))) * "1.35 L"#

#V_1 = "10.834 L"#

Rounded to two sig figs, the number of sig figs you have for the pressure of the tire at #20.0^@"C"#, the answer will be

#V = color(green)(|bar(ul("11 L"))|)#

SIDE NOTE STP conditions are often given as a pressure of #"1 atm"# and a temperature of #0^@"C"#, so if that is how STP conditions were defined ti you, simply redo the calculations using a pressure of #"1 atm"# instead of a pressure of #"100 kPa"#.

Rounded to two sig figs, the answer will come out to be the same, #"11 L"#.