For a 1st order reaction the logarithm of concentration is linear to time. The linear equation of the following curve is lnC = lnC0 – 0.2t; where C is the molar concentration (M) of a reactant, C0 is the molar concentration at time t = 0 (the starting concentration or the initial concentration), and in this particular case C0 = 10 M; and t is time in seconds. What is the slope (and the unit) of the curve? What will be molar concentration of the reactant at time t = 40 sec?
Answer:
Given linear equation for first order reaction is
lnC=lnC0 - (0.2)t
Or lnC=-(0.2)t + lnC0
y=mx+C
[lnC=-kt + lnC0]
Therefore the plot lnC vs time gives slope=-0.2 s^-1=-k
Here k=rate constant=0.2 s^-1.
Given C0=10M, C=? at t=40s.
Therefore lnC=-(0.2s^-1)(40s) + ln10
lnC=-5.697
C=e^-5.697=3.35x10^-3 M
Therefore molar concentration of reactant at t=40s is
C=3.35x10^-3 M.
Please let me know if you have any doubt. Thanks.
For a 1st order reaction the logarithm of concentration is linear to time. The linear equation...
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