*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 d*

*m*^{3}

*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 -1c*)*m*^{3}

*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 = 107.953c*

*m*^{3}

*= 0.10795*

*d*

*m*^{3}

*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)*

*....................................................................................................................................................*

*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 = 0.558Uncertainty RMM = (Max - Min )/number trials = (54.998 - 52.766)/4 = 0.558

*Average RMM = (53.943*

*±0.558) = (53.94*

*±0.56)*

....................................................................................................................................................................................................................................................................................................................

*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*

*.........................................................................................................................................................*

*Detail error analysis and propagation of error done by student 1***.........................................................................................................................................................**

**.............................................................................................................................**

*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*

*T*

*hanks to all pictures and souces used for the above post*
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