) The first-order decomposition of a colored reactant (X) into a colorless Amay)
ID: 544026 • Letter: #
Question
) The first-order decomposition of a colored reactant (X) into a colorless Amay) as a function of time. The following results were obtained: 1x1(M) t(min) 4.00 x 10 3.00 x 105 1.50 x 10 5 0.600 0.200 0.150 0.075 35.0 44.2 a) Recalling that A is proportional to concentration, calculate the initial value of [X b) Calculate the first-order rate constant for the decomposition reaction. c) Calculate the time required for the absorption to decrease from its initial value of 0.600 to 0.075 (that of the last data point). d) Calculate the half-life of the decomposition reaction.Explanation / Answer
a)
since it has linear ratio
[X] vs A is linear so
interpolation -->
slope = (0.20-0.15)/(4*10^-5 - 3*10^-5) = 5000
A = m*C
C = A/m
C = 0.6/5000
C = 0.00012 = 1.2*10^-4 M
b)
1st order constant,
slope = (ln(C) -ln(C0) / (t-t0)
slope = (ln(4*10^-5) -ln(3*10^-5)) / (35-44.2)
slope = -0.03126
k = -slope
k = 0.03126 1/min
c)
ln(C) = ln(C0) - kt
substitute data
A = 0.6 --_> 1.2*10^-4; to 0.075 --> 1.5*10^-5
ln(C) = ln(C0) - kt
ln(1.5*10^-5) = ln(1.2*10^-4) - 0.03126*t
t = (ln(1.5*10^-5) -ln(1.2*10^-4) )/(-0.03126)
t = 66.52 min
d)
half life = ln(2)/k = ln(2) / 0.03126
HL = 22.173min
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