Please help me with a Rate Law problem.?

Question

Okay I've spent nearly an hour on this problem with no luck, please help me and explain how you do this. A reaction of the form aA ----> Product gives a plot of ln[A] vs time in seconds which is a straight line with a slope of -7.35 x10^-3. Assuming 0.0100 M, calculate the time in seconds required for...

Answer 1

if this is your rate law,
ln[A] = -kt + ln[Ao]

and you plot ln[A] on the y axis vs t on the x-axis and you get a straight line, the slope of that line = -k

why? think about y = mx + b.. that's a line with slope = m

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anyway, you can rearrange
ln[A] = -kt + ln[Ao]

into
ln([A] / [Ao]) = -kt

then...
t = ln([A] / [Ao]) / -k

at 80.5% completion,, [A] = 0.195 x [Ao].. so that
t = ln(0.195 [Ao] / [Ao]) / -k

and finally
t = ln(0.195) / (-7.35x10^-3/sec) = 222 seconds

Answer 2

80.5% complete means 19.5% remaining. 19.5% of 0.0100 M equals 0.00195 M

ln 0.00195 = - (7.35 x10^-3) (t) + ln 0.01

-6.24 = - (7.35 x10^-3) (t) + (-4.6052)

1.6348 = (7.35 x10^-3) (t)

t = 222.42 s

Answer 3

Rate Law Problems