topic3kft131-121008010723-phpapp02.pdf - TOPIC 3 KINETIC THEORY OF GASES Examples of Solved Problems 1 Calculate the mean speed <v> and the most

topic3kft131-121008010723-phpapp02.pdf - TOPIC 3 KINETIC...

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12 TOPIC 3- KINETIC THEORY OF GASES Examples of Solved Problems 1. Calculate the mean speed, < v> and the most probable speed, v mp for CO molecules at 100 o C. Solution: 1 2 / 1 3 2 2 2 / 1 1 3 1 1 3 2 / 1 1 3 1 1 2 / 1 531 ) 10 28 ( ) 373 )( 314 . 8 ( 8 ) 10 28 ( ) 373 )( 314 . 8 ( 8 ) 10 28 ( ) 373 )( 314 . 8 ( 8 8 - - - - - - - - - - - = × = × = × = = > < s m kg s m kg mol kg K mol K m Pa mol kg K mol JK M RT v π π π π The unit of the average speed is m s -1 , so to calculate it, we used gas constant, R in unit J K -1 mol -1 (1 J = 1 kg m 2 s -2 ) or Pa m 3 K -1 mol -1 ( 1 Pa = 1 kg m -1 s -2 ) and the molar mass M was expressed in kg mol -1 . 1 2 / 1 1 3 1 1 2 2 2 / 1 471 10 28 ) 373 )( 314 . 8 ( 2 2 - - - - - - = × = = s m mol kg K mol K s m kg M RT v mp (To remember the formula of various speed: most probable speed , v mp which has 2 words before speed , so the formula involve, 2RT ,…..for the root-mean- square speed, which has 3 words, so in the formula involve 3RT .... The most important formula that you will always use is the mean speed, < v> ). Other formula for speeds 1. Relative mean speed between 2 molecule of same type 2 / 1 1 1 2 1 2 1 11 8 2 2 × >= < = > < + > < >= =< M RT v v v v C rel π 2. Relative mean speed between 2 molecule of different type + = + = > < + > < >= =< 2 1 2 1 2 2 2 1 12 ) 12 ( 1 1 8 8 8 M M RT M RT M RT v v v C rel π π π
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13 2 . For 1.00 mol of CH 4 (g) at 400 K and 1.20 atm, calculate: i) the probability density for v y at 90.000 m s -1 ii) the number of molecules whose speed lies in range 90.000 to 90.001 m s -1 . iii) the probability that a molecules’s speed lies between 90.000 to 100.000 m s -1 .
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  • Mole, Kinetic theory

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