What is the volume of one mole
of gas at standard temperature
and pressure? Standard
temperature is 273 K and
standard pressure is 1.01×10^5
Pa.
PV = nRT
V = 2.25×10í^2 m^3
19.6 - Sample problem: tank of air
Scuba divers may carry small tanks like the one shown above to give them air in case of an emergency. Air that is at atmospheric pressure,
1.01×10^5 Pa, is pumped into the tank. The process of filling the tank increases the temperature and pressure of the air. The temperature will
decrease as heat flows from the warmer tank to its cooler surroundings, but we assume the compression process occurs quickly enough for
heat flow to be negligible. A value for atmospheric pressure is stated below.
Scuba diving equipment manufacturers use an estimated breath size of 1.6 liters, so this tank would hold a little over 50 typical breaths.
Assuming a diver might breathe about 15 times a minute, an average under normal conditions, the emergency tank would give her around
three minutes of air. However, she might be breathing a little more rapidly if she needs to use the tank!
Variables
What is the strategy?
- Model the air as an ideal gas. State the ideal gas law, and isolate the parameters that are constant, R and the amount n of gas, on one
side of the equation. - Since the values mentioned above are constant, for both the initial and final states of the gas the “other” sides of the equations are equal
The emergency scuba tank is filled
with 8.50×10í^2 m^3 of air at
atmospheric pressure and 21.0°C.
Immediately after the tank is filled, the
absolute pressure is 1.53×10^7 Pa and
the volume is 8.37×10í^4 m^3. What is
the temperature of the air in the tank
at that time?
initial volume of air V
i = 8.50×10í (^2) m 3
initial pressure P
i = 1.01×10
(^5) Pa
initial temperature Ti = 21.0°C
final volume of air Vf = 8.37×10í^4 m^3
final pressure Pf = 1.53×10^7 Pa
final temperature Tf
moles of air n