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half life

# half life - reaction Rate = k NH 3 = k k = NH 3 = 4.12E-6 M...

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( 8.25E-3 M) / 2 = 4.13E-3 M ( 4.13E-3 M) / 2 = 2.07E-3 M ( 2.07E-3 M) / 2 = 1.04E-3 M Therefore, each time period, t, is a half life. (1) Half life when the starting concentration is 8.25E-3 M: t 1/2 = t = 999 s - 0 = 999 s Half life when the starting concentration is 4.13E-3 M: t 1/2 = t = 1.50E+3 s - 999 s = 501 s The half life goes from 999 s to 501 s . Therefore, the half life is not constant and the reaction is not first order in NH 3 (2) Average rate of disappearance of NH 3 from t = 0 s to t = 999 s : Rate = - [ NH 3 ] = -( 4.13E-3 - 8.25E-3 ) M = 4.12E-6 M s -1 t ( 999 - 0) s (3) Average rate of disappearance of NH 3 from t = 999 s to t = 1.50E+3 s : Rate = - [ NH 3 ] = -( 2.07E-3 - 4.13E-3 ) M = 4.11E-6 M s -1 t ( 1.50E+3 - 999 ) s (4) The rate of disappearance of NH 3 is essentially constant with an average value of 4.12E-6 M s -1 . Therefore, the rate of the reaction does not depend on the concentration of NH 3 and the reaction is zero order in NH 3 . The rate constant for a zero order reaction of the form A products is equal to the rate of the reaction.

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Unformatted text preview: reaction. Rate = k[ NH 3 ] = k k = -[ NH 3 ] = 4.12E-6 M s-1 t Note: The fact that the rate of the reaction is constant is consistent with the the half life decreasing with decreasing concentration. Less must react, so it takes less time. Average (1/[ NH 4 NCO ]) / t from t = 152 min to t = 455 min : 1 = 1 − 1 = 2.915 M-1 [ NH 4 NCO ] 0.171 M 0.341 M (1/[ NH 4 NCO ]) = 2.915 M-1 = 9.62E-3 M-1 min-1 t ( 455- 152 ) min (3) For a second order reaction of the form NH 4 NCO products, a plot of 1/[ NH 4 NCO ] versus t is linear with a slope equal to the rate constant, k. The slope is also expressed as (1/ [ NH 4 NCO ]) / t. Therefore, a change in the reciprocal of the concentration with time is constant. Here it is seen that (1/[ NH 4 NCO ]) / t is essentially constant with an average value of 9.63E-3 M min-1 . Therefore, the reaction is second order in NH 4 NCO , with a rate constant of 9.63E-3 M-1 min-1 ....
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