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Question

At what temperature the most probable speed of SO2 molecules have the same value of root mean square speed of O2 molecules?


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Solution

Step 1: Formula for most probable velocity and root mean square speed

  • The formula of most probable velocity of SO2 =2RTMSO2

WhereR-gasconstantT-TemperatureMSO2-MolecularweightofSO2

  • The root mean square speed ofO2=3RTMO2

WhereR-gasconstantT-TemperatureMO2-MolecularweightofO2

Step 2: Equating most probable velocity and root mean square speed

  • The most probable speed of SO2 = the root mean square speed of O2

2RTMSO2=3RTMO2

  • Squaring on both sides we get,

2xRxTMSO2=3xRxTMO2

Step 3: Finding molecular weight:

ThemolecularweightofSO2=32x2(16)=64ThemolecularweightofO2=2(16)=32

Step 4: Substituting values:

2xRxTMSO2=3xRxTMO22xRxT64=3xRx300322T64=90032T=900K

Hence, at 900K the most probable speed of SO2 molecules have the same value of root mean square speed of O2 molecules


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