# 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

#### Answer:

#### 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

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

So, **STP** conditions are defined as a pressure of *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

Rearrange the combined gas law equation to solve for

#(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

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

**SIDE NOTE** *STP conditions are often given as a pressure of* *and a temperature of* *so if that is how STP conditions were defined ti you, simply redo the calculations using a pressure of* *instead of a pressure of*

*Rounded to two sig figs, the answer will come out to be the same,*