STATES OF MATTER 
properties of gases and liquids (fluids) and solids
18.
Boyles Law gas calculations using P_{1}V_{1}
= P_{2}V_{2}
Practice questions  problem solving using Boyle's Law.
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chemistry revision notes: basic school chemistry science GCSE chemistry, IGCSE chemistry, O level
and ~US grades 8, 9 and 10 school science courses or equivalent for ~1416 year old
science students for national examinations in chemistry and also helpful for UK
advanced level chemistry students aged ~1618 and US grades 1112 K12 honors.
18,
The particle model of a gas  and gas pressurevolume calculations using Boyle's
Law

Explanation
of Boyle's Law 
All
particles have mass and their movement gives them kinetic energy and
momentum.

The particles in a gas are in constant
random motion  random direction, variety of velocities and kinetic
energies.

When the fast moving gas particles
collide with a surface, their millions of impacts create a force that we
measure as gas pressure  the total force of impacts per unit area.

The particles collide with the container
surface completely at random and impact at every angle, BUT, the effect is
to create a net force at right angles to the surface  gas pressure!

The greater the number of collisions per unit area of surface,
the greater the pressure, assuming the gas volume and temperature are kept constant.

If the temperature is kept constant and
the volume increased, the impacts are more spread out and less frequent per
unit area, so the gas pressure decreases.

Conversely, if a gas is
compressed into a smaller volume at constant temperature, the number
of impacts per unit area increases, so the pressure increases.

From measurements of volumes and
pressure of gases at constant pressure, a numerical inverse law can
be formulated  Boyle's law.

pressure x volume = a constant
(at constant temperature)

pV = constant
(at constant temperature)

The standard units of pressure
and volume are:

p = pressure in pascals (Pa),
V = volume (m^{3})

You can connect two pressure and
two volumes by the simple equation

p_{1} x V_{1}
= p_{2} x V_{2}

where 1 represent the original
conditions of the gas in terms of pressure and volume, and 2 the final situation if an enforced change of p_{1}
or V_{1} is made.

Examples of simple gas
calculations

(i) 5 m^{3} volume of
a gas at a pressure 101 300 Pa was compressed to a volume of 2.8
m^{3}.


Calculate the final
pressure.

p_{1} x V_{1}
= p_{2} x V_{2}

rearranging gives p_{2}
= (p_{1} x V_{1}) / V_{2}

p_{2} = (101 300
x 5) / 2.8 = 180893 Pa

(ii) 10m^{3} of gas
at a pressure of 100 000 Pa was compressed to a pressure of 300
000 Pa.


Calculate the final
volume of the gas.

p_{1} x V_{1}
= p_{2} x V_{2}

rearranging gives V_{2}
= (p_{1} x V_{1}) / p_{2}

V_{2} = (100 000
x 10) / 300 000 =
3.33 m^{3}
More on gas pressure and volume calculations
AND some practice questions for you to do, answers at end of page!
Boyle's Law for volume and gas
pressure

The particle theory of gas pressure
was explained above
so this section concentrates on the gas law
calculations involving pressure and volume.

Boyle's Law states that for given mass of gas
at a constant temperature (^{o}C or K), the product of the pressure multiplied by the
volume is a constant.

p x V = constant

Therefore, for initial
values of p_{1}
and V_{1}, which change to final values of p_{2} and V_{2}, the following
equation applies ...

p_{1} x V_{1}
= p_{2}
x V_{2} (for fixed amount of gas at constant
temperature)

or
p_{2}
= p_{1}
x V_{1}/V_{2}_{ }or V_{2}
= p_{1} x V_{1}/p_{2}

The graph shows how the pressure and volume
vary according to Boyles Law at two different temperatures.

At lower temperatures the volume and pressure
values are lower (see next section).

You can use any volume or
pressure units you like as long as both p's and both V's have the
same units.

Using particle theory and
simple arithmetical values to explain Boyles Law.

If a gas is compressed to half its
original volume the concentration or density of the gas is doubled. Therefore
there will be twice as many collisions with the surface causing twice the
impact effect i.e. double the pressure.

If the volume of a gas is
increased by a factor of three, the concentration is reduced by the same
factor, so the chance of particle collision with the container walls is
similarly reduced, so the pressure decreases by a factor of three.

Gases e.g. oxygen for hospitals, can be
stored under high pressure enabling reasonably efficient storage. Because
the internal pressure in the cylinder is so much greater than the external
pressure, on fitting a valve, a large volume of gas can be released to flow
slowly under controlled conditions for a patients respiration.

Examples of Boyle's Law calculations (constant temperature assumed)

Ex. Q 1

Ex. Q2

Ex. Q3

A 100 cm^{3} gas syringe
containing 80 cm^{3} of gas that was compressed to 60 cm^{3}.
If atmospheric pressure is 101325 Pa, and the temperature remains constant,
what is the pressure of the gas in the syringe after compression?



Ex. Q4
ANSWERS
Learning objectives
for Boyle's Law calculation for the
pressure and volumes of gases
Know the mathematical
relationship between pressure and volume of a fixed mass of gas at a
fixed constant temperature.
Know P1 x V1 = P2 x V2 and
be able to rearrange the formula and perform calculations using Boyle's
Law.
Be able to use the kinetic particle theory to explain Boyle's Law in
terms of increasing or decreasing the number of particle impacts per
unit area.
Know how to use units of
pressure (usually Pascals Pa) and volume (usually cubic metres m^{3}).
BUT, be able to use
other units like atm, dm^{3} (litres) or cm^{3}.
AND remember in Boyle's
Law calculations, make sure you use the same pressure units for P1 and
P2 and the same volume units for V1 and V2, otherwise you cannot deduce
or work out any correct answer!
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