Monday, October 17, 2011

IB Chemistry uncertainty error calculation for RMM, propagation of error and standard deviation

Uncertainty Calculation for RMM of butane gas using ideal gas equation


Uncertainty Calculation for RMM using Ideal Gas Equation.
Ideal gas law equation,  PV = nRT

P - absolute pressure of the gas in kPa
V - volume in dm3
n - number of moles
T - absolute temperature.(Kelvin)
R = gas constant, 8.314 J K-1 mol-1


PV = nRT,     n = mass / RMM
PV =  (mass/RMM) x RT 
RMM = (mass x RT) / PV
To determine RMM of gas - need to find out
  • average mass of gas
  • average volume of gas
  • temp - 296.05K and pressure - 101.760kPa
Data collection by two students. Which is appropriate and correct?
Data by student 1:
Student 1 took average mass for 5 trials shown above
  • Average Mass for gas = Average mass (flask + gas) - Average mass (flask + air) + Mass air
  • Average Vol gas = Average vol of water = Average mass water (density water 1g -1cm3)
Calculate the RMM of a gas, given
Average mass gas = Average mass (flask + gas) - Average mass (flask + air) + Mass for air
Average mass gas = (55.734 - 55.610 + 0.129) = 0.253g


Average Vol gas = Average Vol of water = Average Mass water = 107.953g = 107.953cm3 = 0.10795dm3
Results on how to determine mass of air is shown below
RMM gas = (mass x RT) / PV 
RMM gas =  (mass x R x T) / PV    average mass gas = 0.253    average vol gas = 0.10795dm3
RMM gas =  ( 56.6 ±2.56%) converted to absolute uncertainty = (56.6 ±1.45)= (56.6±1.4)
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Data by student 2
Did not take average mass or volume of gas
  • Find mass, vol and calculate RMM for trial 1
  • Find mass, vol and calculate RMM for trial 2
  • Find mass, vol and calculate RMM for trial 3
  • Find mass, vol and calculate RMM for trial 4
Calculated average RMM for 4 trials
Average RMM = 53.943








How to calculate uncertainty for average RMM?
RMM 1=(54.998 ±0.1890) RMM 2= (54.775±0.1883) RMM= (52.766±0.1814) RMM=53.232±0.1830


Wrong way to calculate uncertainty for RMM
  • NEVER take the average of uncertainty - (0.1890 + 0.1883 + 0.1814 + 0.1830)/4 = 0.1854
  • WRONG ANSWER = (53.943 ±0.1854) = (53.94±0.18)
Right way to calculate uncertainty for RMM
RMM 1=(54.998 ±0.1890) RMM 2= (54.775±0.1883) RMM= (52.766±0.1814) RMM=53.232±0.1830

1st method using std deviation for 4 diff RMM = (53.943±1.109) = (53.94±1.11)
Average RMM = (53.94±1.11)

2nd method using Max/Min error 
Max RMM = 54.998        Min RMM = 52.766
Uncertainty RMM = (Max - Min )/number trials = (54.998 - 52.766)/4 = 0.558 

Average RMM = (53.943±0.558) = (53.94±0.56)
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Which data is better and is there a better way to collect data.


Student 1 
  • average mass and average vol
  • only 1 RMM is calculated
Student 2
  • one mass and one vol to find RMM
  • average RMM is calculated



Student should perform both ways using average mass and average vol and also average RMM.
  • Use student 1 method to collect average mass and average vol and find RMM
  • Perform expt 3 time (triplicate) to obtain 3 different RMM
  • Find the average RMM using student 2 method
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Detail error analysis and propagation of error done by student 1


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    Simple Experimental setup
    Determination of (RMM) of a gas ( Butane ) using ideal gas equation.
    Steps to follow
    1. Weigh a dry 100ml volumetric flask with stopper to 0.001g
    2. Remove stopper
    3. Fill it with CO2/butane gas with glass delivery tube, stopper it and reweigh
    4. Repeat step 2 and 3 until mass of flask is constant
    5. Fill the flask with water, insert a stopper, and reweigh it.
    Click Here for IA on DCP and CE
    Detail Experimental Setup
    Click Here to view detail procedure setup.
    Source from Chemistry SLSS website
    Click HERE for more sample ideal gas calculation
    Click HERE for more info on ideal gas equation
    Thanks to all pictures and souces used for the above post

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