Gas_Laws - slider-dpchemistry-11

```Year 11 DP Chemistry
Rob Slider
Units
Volume (V)
Pressure (P)
Temperature (T)
SI unit: m3
SI unit: Pa (pascal)
SI unit: K (Kelvin)
1m3 = 1000 dm3 = 1000L
atm (atmosphere) – the
pressure acting on an object
on Earth (standard pressure)
K = 0C + 273
1atm = 1.013 x 105 Pa
Absolute zero = 0K or -2730C
1kPa = 103 Pa
F.P. (water) = 273K or 00C
1dm3 = 1000cm3 = 1000mL
1atm = 101.3 kPa
0C
= K - 273
Law of Combining Gas Volumes
The volume of gases taking part in a chemical reaction show simple whole number ratios to one another
when those volumes are measured at the same temperature (T) and pressure (P)
When gases are at the same T & P, theMolar
same volume
of anyof
gasahas
the same amount of particles (moles)
Volume
Gas:
At stp, 1 mole of any gas occupies 22.4dm3
Example
Practice Problem
 The molar ratio of the following reaction to
 The molar and volume ratios of the following
(stp is 273K and 101.3kPa)
produce ammonia gas is 1:3:2.
reaction are 2:1:2 since the reactants and
products are gases.
N2(g) + 3H2(g) -----> 2NH3(g)
2H2(g) + O2(g) -----> 2H2O(g)
Since all the reactants and products are gases,
the mole ratio is the same as the ratio of the
So, if there is 50mL of hydrogen gas, what are
volumes of gases.
the volumes of oxygen gas and water vapour?
So,
50mL of hydrogen gas would react with
10mL of nitrogen gas reacts with
50 x ½ = 25mL oxygen gas to produce
10 x 3 = 30mL of hydrogen gas to produce
50mL of water vapour
10 x 2 = 20mL ammonia gas
Note all of the reactants/products are gases
Exercises 1
1.
Find the volume occupied by 8g of oxygen gas at STP.
5.6 dm3
2.
How many cm3 are there, at STP, in 1.72 g of phosphorous
pentoxide (P2O5)?
271 cm3
3.
What is the mass of 3.2 dm3 of nitrogen gas measured at
STP?
4.0 g
4.
Find the mass of 275 cm3 of phosphorous trichloride gas
1.69 g
measured at STP.
Boyle’s Law (P vs V)
At constant temperature:
Volume of a given quantity of gas is inversely proportional to pressure: V= 1/P
(E.g. if the volume of a gas is doubled, its pressure is halved.)
OR
The product of a gas’s volume and its pressure is a constant : PV = constant, PV = k
So, at constant temperature for a given quantity of gas : PiVi = PfVf
where,
Pi and Vi are the initial pressure and volume,
Pf and Vf are the final pressure and volume.
Note: pressures and volumes must be in the same units of measurement on each side.
Ideal vs. Real gases
All gases approximate Boyle's Law at high temperatures and low pressures.
Ideal Gas - a hypothetical gas which obeys Boyle's Law at all temperatures and pressures
Real Gas - approaches Boyle's Law behaviour as the temperature is raised or the pressure
lowered.
Boyle’s Law – inversely proportional
Note how the
volume changes in
relation to the
pressure exerted on
a gas.
At a given
temperature, this
relationship is
predictable for an
ideal gas.
Twice the pressure (P2) = half the volume (V2)
Boyle’s Law - Graph
P vs V gives a parabolic shape
V vs 1/P gives a linear shape
Exercises 2
1.
A sample of 200 cm3 of a gas has a pressure of 1.00 atm.
The pressure is increased to 1.10 atm at a constant
temperature. Find the new volume of the gas. 182 cm3
2.
180 mL of a gas is compressed to 135 mL with no change in
temperature. If the original pressure was 1.05 x 105 Pa,
what is the new pressure?
1.40 x 105 Pa
3.
2.70 dm3 of gas was originally at a pressure of 1.20 atm.
Under constant temperature conditions, what pressure in
kPa would be needed to change the volume to 2.50 dm3?
131 kPa
Charles’ Law (T vs V)
At constant pressure,
Volume of a given quantity of gas is directly proportional to the absolute temperature : Vα T (in
Kelvin)
(E.g. if the temperature (K) is doubled, the volume of gas is also doubled.)
OR
The ratio of its volume and the absolute temperature is a constant : V/T = constant, V/T = k
So, at constant pressure: Vi/Ti = Vf/Tf
where,
Ti and Vi are the initial temperature and volume,
Tf and Vf are the final temperature and volume.
Note: Ti and Tf must be in Kelvin NOT Celsius. (temperature in Kelvin = temperature in Celsius + 273)
(approximately)
Ideal vs. Real gases
All gases approximate Charles' Law at high temperatures and low pressures.
Well above it’s condensation point, the volume of a real gas decreases linearly as it is cooled at constant
pressure. However, as the gas approaches the condensation point, the decrease in volume slows down.
At condensation, the gas turns to a liquid and, therefore, does not obey Charles’ Law
Absolute zero (OK) is the temperature where the volume of a gas would theoretically be zero if it did not
condense.
Same pressure
Note how the volume
changes in relation to
temperature with constant
pressure applied
Increase the temperature and
the volume goes up
At a given pressure, the
pressure is directly
proportional to the volume.
(As temperature goes up, so
does the pressure)
Try this: fill a balloon with air, then put it in the freezer. What
happened? How does this demonstrate Charles’ Law?
Charles Law - Graph
Volume is directly proportional
to absolute temperature (linear)
Extrapolate this relationship back to
absolute zero where the volume of a gas is
theoretically zero and all molecular motion
stops. Is this possible?
Exercises 3
1.
A given sample of gas has a volume of 5.0 m3 at a
temperature of -230C. What volume would it occupy at
300 K assuming the pressure remains constant? 6.0 m3
2.
360 cm3 of a gas is heated from 00C to 910C. Assuming no
480 cm3
pressure change, find the new volume.
3.
When heated under constant pressure, the volume of a
gas increased from 2.42 dm3 to 2.67 dm3. If the initial
temperature was 190C, find the final temperature in 0C.
490C
Gay-Lussac’s Law (P vs T)
At constant volume,
Pressure of a given quantity of gas is directly proportional to it’s
temperature
OR
the ratio of pressure and temperature is equal to a constant p/T = k
(a constant)
So, at constant volume: pi/Ti = pf/Tf
where,
pi and Ti are the initial pressure and temperature,
pf and Tf are the final pressure and temperature.
Note: pressures and temperature (Kelvin) must be in the same units of
measurement on each side.
Gay-Lussac’s Law
Note the effect
that increased
temperature has
on the pressure
of the container
which is at
constant volume.
An increase in temperature leads to increased pressure
Gay-Lussac - Graph
Note how
pressure
increases as the
temperature
increases as the
average kinetic
energy of the
particles exerts
more force on a
container of
constant volume
How does this photo relate to
Gay-Lussac’s Law??
Exercises 4
1.
At a given temperature of 70C, a sample of gas has a
pressure of 1.40 atm. If it is heated to 320 K, while the
volume stays constant, what would the new pressure be?
1.60 atm
2. The pressure of a gas is reduced from 102.5 kPa to 97.5 kPa.
If the volume does not change, calculate the final
temperature in Celsius if the initial temperature was 150C.
10C
3. A sample of gas has an initial temperature of 100C. If the
pressure is doubled, find the resulting temperature in
Celsius assuming constant volume.
0
293 C
Combined Gas Law
If we combine all three individual gas laws into one, we can show how pressure,
temperature and volume are related in one equation.
pi V i =
Ti
pf Vf
Tf
Temperature must be in Kelvin. Pressure and volume can be in any unit as long
as they are the same on both sides of the equation.
This equation can be used if there is more than one variable changing at once.
Exercises 5
1.
A gas sample of 32.0 cm3 has a pressure of 1.05 atm and a temperature
of 27.00C. What would be the volume of the gas at a pressure of 1.12
atm and a temperature of 7.00C?
28 cm3
2.
At 0.75 atm and -230C a gas has a volume of 100 cm3. Find the volume
at STP.
3
82 cm
3.
A sample of gas occupies 0.654 m3 at 1.14 atm and 90C. Calculate the
volume at STP.
0.722 m3
4.
When measured at 103.5 kPa and 22.00C, some gas has a volume of
232 mL. What would be the volume in litres at STP?
0.219 L
Ideal Gas Law
An Ideal Gas (perfect gas) is one which obeys Boyle's Law, Charles' Law and G-L’s Law exactly.
 An Ideal Gas obeys the Ideal Gas Law (General gas equation):
PV = nRT
where,
P=pressure,
V=volume,
n=moles of gas,
T=temperature,
R=the gas constant (dependent on the units of pressure, temperature and volume)
R = 8.314 J K-1 mol-1
R = 0.0821 L atm K-1 mol-1
P is in (Pa), V is in (m3), T is in (K) (note: J = m3Pa)
P (atm), V (L), T (K)
Presumptions – Is any gas ideal?

Presumptions of an Ideal Gas according to Kinetic Theory of Gases:





Real Gases deviate from Ideal Gas Behaviour because



Gases consist of molecules which are in continuous random motion
The volume of the molecules present is negligible relative to the total volume
occupied by the gas
Intermolecular forces are negligible
Pressure is due to the gas molecules colliding with the walls of the container
at low temperatures the gas molecules have less kinetic energy (move around less)
so they do attract each other
at high pressures the gas molecules are forced closer together so that the volume of
the gas molecules becomes significant compared to the volume the gas occupies
The Overall Presumption
 Under ordinary conditions, deviations from Ideal Gas behaviour are so
slight that they can be neglected. A gas which deviates from Ideal Gas
behaviour is called a non-ideal gas.
Gas Law Summary
Boyle’s Law
PiVi = PfVf
Gay-Lussac’s Law
pi/Ti = pf/Tf
Charles’ Law
Vi/Ti = Vf/Tf
Ideal Gas Law
pV = nRT
Exercises 6
1.
5 moles of a gas at 250C and 1.15 atm occupies what volume?
2. Magnesium reacts with hydrochloric acid to produce
hydrogen gas and magnesium chloride
What volume of gas is evolved at 273 K and 1 atm pressure
when 0.623 g of Mg reacts with 27.3 cm3 of 1.25 mol dm-3
hydrochloric acid.
b) Calculate the volume occupied by the hydrogen gas evolved if it
is collected at 220C and 1.12 atm pressure.
c) If the actual volume of hydrogen collected was 342 cm3, what
is the percentage yield?
a)
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