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Observations:
Reported Air Pressure: 102.8 kPa
Correction for Altitude: 102.8 kPa - 1.2(85/100)=101.6kPa
Mass of Mg
used (g)
Moles of
Mg used
Room Temp.
(oC)
Room Press.
(kPa)
Water Temp
(oC)
Vol. of Gas
Collected (mL)
.04
.04/24.31
= .00165
22
101.6
22
= 295 K
25
= 0.025 L
Calculations:
1) Write the balanced chemical equation for this lab: Mg(s) + 2HCl(aq) —> MgCl2(aq) + H2(g)
2) Based on the equation, what is the theoretical yield, in moles, of H2 gas for your reaction?
0.00165 mol Mg(s) /2 x1 = 0.000825 mol H2(g)
3) a) What is the partial pressure of water in the cylinder (PH2O) based on room temperature? 2.3 kPa
Look up the value for 22 oC in the table on page 464 in the text book (2.3 is what I remember)
b) If no gases except H2 and H2O are present, what is the partial pressure of Hydrogen gas (PH2)?
PT = PH2 + PH2O thus, PH2 = PT - PH2O = 101.6 - 2.3 = 99.3 kPa
Discussion:
1. For what two reasons must you wait 5 minutes before measuring the gas volume in the cylinder?
Several reasons: 1) let the gas temperature in the tube to equilibrate with the room temperature, 2)
let the gas in the tube reach 100% humidity, and, as one of you pointed out, 3) make sure the
reaction really is over (and all the gas has collected at the top of the tube)
2. Use the combined gas law to calculate the volume your hydrogen gas by itself would have occupied
at SATP? (P1 is PH2 from data, V1 is from the data table, and T1 is the room temperature)
P1V1/(n1T1)=P2V2/(n2T2) therefore: V2 = n2T2P1V1/(P2n1T1)
= T2P1V1/(P2T1) since n is not changing
= 298K x 99.3kPa x 0.025L /(100kPa x 295K)
= 0.0251 L
Not much of a difference since we already were close to SATP conditions during the lab.
3) a) Should one mole of any ideal gas have the same volume at SATP? Yes.
b) What is the accepted value of the ideal gas constant (R)? 8.31 kPaL/molK
4) a) Use the ideal gas equation, PV=nRT, to calculate your experimental value for R
Use the volume that you calculated for SATP in question 2
R = PV/nT = (100 kPa)(0.0251)/((0.00165 mol)(298 K)) = 2.51/.4917 = 5.10
b) Calculate the percent discrepancy between your molar volume at SATP and the theoretical one
100% (5.10 - 8.31)/8.31 = -39%
not so great!
5) Use the ideal gas law and the accepted value of R to calculate what volume 1 mole of ideal gas
should have at SATP.
V = nRT/P = 1(8.31)(298)/100 = 24.71 L
Gas Concepts
Ideal gas molecules have large kinetic energies such that the intermolecular forces have virtually zero
effectiveness at holding molecules together. Thus:
1) molecules move in straight lines in random directions unless they collide with something.
2) all collisions are elastic - no kinetic energy is lost.
3) the volume of the molecules is insignificant compared to the total volume of the gas.
Properties needed to calculate the number of moles of a gas:
Volume
Temperature: a measure of the average internal kinetic energy of the particles in an object
A given temperature actually corresponds to a distribution of kinetic energies.
Note just how fast air molecules move on average,
even at room temperature (300 K): 500 m/s
or 0.5 km/s.
Higher temperatures mean higher average speed.
However, temperature is proportional to kinetic
energy, not speed.
Ek = .5 m v2
At the same temperature, molecules with larger molar masses are moving more slowly.
You can measure this by releasing two gases at the same moment and timing how long it
takes for their odours to be detected at some distance away.
v12/v22 = m2/m1 = t22/t12
Pressure:
pressure is calculated as a force divided by the area over which it is applied
in a gas: the force is the sum of the collisions happening at any given moment
they are small, but as noted above, they move fast and they are many
the area is the internal surface area of the container
More moles of gas molecules means more collisions per second = higher pressure
Higher temperature, the faster the molecules, the more often collisions occur and the
greater the force of the collisions = higher pressure
With some simple experiments, we can derive a mathematical relationship between moles,
temperature, pressure, and volume that we can use.
Real gases condense as pressure increases or temperature decreases. At that point, they stop behaving
in an ideal fashion.
Since direct relationships can be described between all four of these properties, we can derive:
P1V1
n 1 T1
=
P2V2
n 2 T2
P1V1/(n1T1) = P2V2/(n2T2)
or
Temperature must be in Kelvins, or the equation will not work. Kelvin = oC + 273
The gas also must be approximately ideal.
P1V1/(n1T1) = P2V2/(n2T2) can be used to calculate how any one of these properties changes if you
know how the other three have changed.
E.g., if the pressure, temperature, and number of moles of gas change, what is the new volume?
V2 = n2T2P1V1 / (P2n1T1)
However, the equation P1V1/(n1T1) = P2V2/(n2T2) means that PV / (nT) = a constant
With experiments, we find that it is the same constant not matter what gas is used, as long as it behaves
as an ideal gas: PV / (nT) = R = 8.31 kPaL/molK
Pressure must be in kPa, volume in L, temperature in Kelvins, and the gas is ideal.
Mixtures of Gases
Since all ideal gases behave ideally, they all contribute to pressure in the same way at the same
temperature. So, at a give temperature in the same container, we would get the same pressure from 5
moles of Nitrogen gas as we would from 2 moles of Nitrogen gas and 3 moles of Oxygen gas.
In the second case, the nitrogen would account for 40% of the pressure (2/5) and the Oxygen would
account for 60% of the pressure.
The pressure produced by just one gas in a mixture (its part) is called Partial Pressure.
Partial pressure is shown with a subscript denoting the particular gas: PN2 and PO2 in the example above.
Total pressure is just P
In general: Px = (nx/ntotal)P
P = Px + Py + Pz... (the total pressure is the sum of all the partial pressures in a mixture)
Water Vapour
This is not an ideal gas at room temperature, since it is well below its boiling point.
There are tables (see page 464) that tell us what the partial pressure of water vapour is at certain
temperatures when the humidity is 100% (a saturated solution of water vapour in air). We encounter
this when we are collecting gases by downward displacement of water.
If we collect 0.05 L of H2 gas at 25 oC and a pressure of 105 kPa by downward displacement of water
in a tube, we can find that the PH O is 3.17 kPa.
We know that P = PH + PH O so PH = P - PH O = 105 - 3.17 = 101.83 kPa
2
2
2
2
2
I can now use the ideal gas equation to calculate the number of moles of hydrogen gas collected
PV=nRT nH = PH V/RT = 101.83 x 0.05 / (8.31 x (25 + 273)) = 0.0021 moles
2
2