4. Gas laws Flashcards
What is a gas?
A gas is a substance that
exists above its critical temperature.
This term is usually used colloquially
to describe a substance whose
critical temperature is below room temperature.
What is critical temperature (CT)?
This is the temperature
above which a gas
cannot be liquefied by the
application of pressure alone
(CT for O2 is −119 °C and N2O is 36.5 °C).
What is an ‘ideal gas’?
An ‘ideal gas’ is a
theoretical gas in
which the molecules behave
as individual particles that move
in a random manner
independent of each other
and
of any inter-molecular forces.
At standard temperature and pressure
(STP: 273.15 K and 101.3 kPa)
most gases behave qualitatively
like an ideal gas.
The ‘ideal gas’ is a useful concept
because it obeys the ideal gas laws.
What are the gas laws?
The gas laws are a set of rules that govern the relationship between thermodynamic temperature, volume and pressure of ideal gases.
> Boyle’s law:
At a constant temperature,
the absolute pressure
of a given mass of gas is inversely
proportional to the volume.
(density = mass/volume
→ density ∝ 1/volume
→ pressure ∝ density)
P oc -> 1/V or PV = Constant
Charles’s law
At a constant pressure,
the volume of a given mass
of gas is
directly proportional
to the absolute temperature.
V oc T or V/T = Constant
> Gay-Lussac’s law:
At a constant volume,
the absolute pressure
of a given mass of gas varies
directly with the absolute temperature.
This is also known as the third perfect gas law.
P oc T or P/T = Constant
Ideal Gas Equation
All of these laws have been united into one,
the Ideal Gas Equation,
which comes from the premise
that in an ideal gas,
a given number of particles
will occupy the
same volume
at a given temperature and
pressure.
PV/ T =Constant
Using this equation,
it is possible to convert one set of conditions
to another because for a given mass of gas:
P1V1 P2V2
____ = ____
T1 T2
> The ideal gas equation
PV = nRT
Where:
n = number of moles of gas present
R = universal gas constant = 8.32144 J/K/mol
What is Avogadro’s hypothesis?
> This states that
equal volumes of gases
at a given temperature and pressure
contain the same numbers of molecules.
> One mole of a gas
at STP will occupy
22.4 L and will contain 6.022 × 10^23 particles (Avogadro’s number).
What is Avogadro’s number?
> One mole of a substance contains the same number of particles as there are atoms in 12 g of carbon-12
(i.e. 6.022 × 1023).
> This number of particles is known as Avogadro’s number.
Give an example where we may
use Avogadro’s hypothesis
Avogadro’s hypothesis is
used to calculate the contents
of a N2O cylinder:
No. of moles of N2O in cylinder =
Weight of N2O \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ Molecular weight of N2O
= (Cylinder weight – Tare weight)
______________________
44
Volume of N2O available (L) = No. of moles × 22.4 L
What are the clinical applications of these gas laws?
The ideal gas law
(P1.V1/T1 = P2.V2/T2)
is used to calculate the volume of O2
available from an O2 cylinder:
> Cylinder capacity is fixed = 10 L [V1]
> Gauge pressure of cylinder =13 700 kPa
> Absolute pressure of cylinder = gauge pressure (13 700 kPa) + atmospheric pressure (100 kPa) = 13 800 kPa [P1]
> Volume of O2 available = [V2]
> Absolute pressure of atmosphere =100 kPa [P2]
> As temperature is constant,
T1 = T2 and hence equation is further
simplified
P1 × V1 = P2 × V2
→ 13 800 × 10 = 100 × V2
→ V2 = 1380 L
> But 10 L will always remain in the cylinder,
and hence 1370 L of O2 is
available.
An alternative approach to this is to use the ideal gas law (PV/T = nRT ) to calculate the contents of a gas cylinder:
> Volume of the cylinder is fixed
> R is a constant
> Temperature is fixed
> Therefore, pressure is directly related to the number of moles of gas
(which can be converted into a volume using Avogadro’s hypothesis).
The ideal gas law is used in the adiabatic process:
> If heat energy is not added to or lost from a system, a rapid compression of gas will result in a rise in its temperature, and conversely a sudden expansion will result in a fall.
> This principle is harnessed by the cryotherapy probe used to freeze lesions in surgery where a sudden expansion of gas through the end leaves its tip extremely cold.
What is Dalton’s law of partial pressures?
This states that the total pressure exerted by a gaseous mixture is equal to the sum of the partial pressures of each of the individual gases within that mixture
What is Henry’s law?
This states that the amount
of gas dissolved in a liquid
is proportional to its partial pressure
above that liquid at a given temperature
(the warmer the liquid,
the less gas that dissolves in it,
and that is why boiling water bubbles
because air comes out of the liquid phase
