Thursday, July 28, 2011

IB Chemistry, IB Biology on uncertainty calculation, random error, standard deviation and error analysis

Uncertainty Calculation for Rate of reaction, Enthalpy Change and Ideal Gas Equation.


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


P - absolute pressure of the gas in Pa /Nm-2
V - volume in m3
n - number of moles
T - absolute temperature.(Kelvin)
R = gas constant, 8.314 J K-1 mol-1
Calculate the RMM of a gas, given
M1, mass empty flask, = (25.385 ±0.001)g
M2, mass flask filled with gas, = (26.017 ±0.001)g
M3, mass flask with water, = (231.985 ±0.001)g
Temperature = 32.0C = (273.0 +32.0) = (305.0 ±0.1)K
Atmospheric pressure = 101,000 Nm-2 /Pa
PV = nRT,     n = mass/ RMM
PV =  RT x mass/RMM 
RMM = RT x mass / PV

Mass of gas = (M2 - M1) = (26.017 - 25.385)g = 0.632g
Vol of gas = Vol of flask = Vol of water = Mass of water = (231.985 - 25.385) = 206.6 x10-6 m3
RMM = RT x mass / PV 
RMM = 8.314 x 305.0 x 0.632 / 101,000 x 206.6 x10-6
RMM (expt value) = 76.80    RMM (actual value) = 80.00


Percentage Error 
= RMM (actual) - RMM (expt) /RMM (actual) x100%
= (80.00 - 76.80)/80.00 x 100%
= 3.20/80 x 100% = 4% (Error)
    
Percentage Uncertainty due random error ( Temp, Mass and Vol )
% Uncertainty Temp = (0.1/305.0 x 100)% = 0.0327% = 0.33%
% Uncertainty Mass gas = (0.002/0.632 x 100)% = 0.32%
% Uncertainty Vol = (0.002/206.6 ) x 100% = 0.000968% = 0.001%
Total % Uncertainty due to random error = ( 0.33 + 0.32 + 0.001 )% = 0.651% = 0.65%
Conclusion:
  • 4% error is more than the total error due to all random error (T, Vol and Mass)
  • Systematic error have to account for the 3.35% difference which might be due to experimental procedure.
  • RMM = (76.8 ± 0.65%) in percentage uncertainty
  • RMM = (76.8 ± 0.5) in absolute uncertainty, max/min range is ( 76.3----77.3)
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    Simple Experimental setup
    Determination of (RMM) of a gas ( CO2 or 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
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    Uncertainty Calculation on Rate of reaction

    IB Chemistry, IB Biology on Uncertainty calculation, error analysis and standard deviation on rate of reaction
    Conclusion:
    • 3 ways to calculate uncertainty for rate of reaction
    • 1st method - using % percentage uncertainty method( most common)
    • 2nd method - using Max/Min method
    • 3rd method - using standard deviation method
    .........................................................................................................................................
    Uncertainty Calculation on Enthalpy Change 
    (Displacement Reaction)

    Conclusion:

    • 2 ways to calculate Uncertainty for Enthalpy Change (ΔQ)
    • 1st method - using % percentage uncertainty method
    • 2nd method - using Max/Min method
    Thanks to all pictures and souces used for the above post

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