Determination of the Rate Law for the Reaction of Methyl Blue with
Sodium Hydroxide
Purpose: The rate law for the reaction of Methyl Blue with sodium hydroxide is to
be measured. The Methyl Blue concentration will be obtained by measuring the
time-dependent absorbance at 586 nm. By determine the time dependence of the
absorbance in the limit where [OH-] >> [MB+] the order with respect to the methyl
blue will be determined by analyzing the time dependence and comparing it to the
expected time dependence for zeroth, first and second order reactions. By
measuring the time dependent absorbance at 2 different hydroxide concentration
the order with respect to [OH-] will be determined. Finally by conducting the
reaction over a range of temperatures the collision factor A and the activation
energy Ea will be determined by plotting ln(k) vs 1/T.
Procedure:
Part A: Calibrating and Measurement of the Methyl Blue visible absorption
spectrum
After calibrating the spectrometer, the absorbance spectrum for 0.0025M Methyl
Blue was recorded using a Vernier SpectroVis Spectrometer and a PC running
LoggerPro 3.0 software. The spectrum is shown in Fig. 1
Figure 1: Absorption Spectrum for Methylene Blue
MB was found to absorb between 500-700 nm with a strong peak at 586 nm. It was
the time-dependent Absorbance at 586 nm that was monitored in Parts B, C
Part B.1: Determining the order with respect to the MB+
To determine the order of the reaction with respect to the MB+, the absorbance of
the MB+ at 598 nm was monitored for the reaction of 10 mL of 0.0025M Methylene
Blue with 10 mL of 0.1M sodium hydroxide for a period of 100 s following the
mixing of the reactants. All reactants volumes were pipetted.
Because the hydroxide concentration remains essentially constant
-
x
y
D
éë MB + ùû = k(T ) éë MB + ùût éëOH - ùût
Dt
{
y
}
» k(T ) éëOH - ùû o éë MB + ùût
= k '(T ) éë MB + ùût
x
x
where
k '(T ) = k(T ) éëOH - ùû o
y
The time-dependent rate is solely due to the time dependent concentration of the
methyl blue. From Beer’s law the absorbance A is directly proportional to the [MB+]
A = ( e l ) éë MB+ ùû
Table 1: Finding the order with respect to Methyl Blue (x) from the time dependent absorbance
X
0
plot
A vs t is linear
slope
-k(T ) éëOH - ùû o
y
1
Ln(A) vs. t is linear
-k(T ) éëOH - ùû o
y
2
1/A vs. t is linear
k(T ) éëOH - ùûo
y
In Fig. 2-5 A vs t, ln(A) vs. t, and 1/A vs. t are shown. Of these it is only the lnA vs. t
that is linear, consequently the reaction is first-order with respect to methylene
blue.
Figure 2: A plot of the absorbance vs. time for the reaction of methylene blue and sodium hydroxide. The
decay of the absorbance is clearly not linear. The reaction is not zeroth order with respect to methylene
blue
Figure 3: A plot of ln(A) vs time for the reaction of Methylene blue and sodium hydroxide. The natural
logarithm of the absorbance is linear with time, therefore the reaction is first order with respect to the
methyl blue
Figure 4: A plot of 1/Absorbance of methylene blue with time, clearly the relationship is not linear, so
the reaction of methylene blue with sodium hydroxide is not second order with respect to the methylene
blue
Part B.2: Determining the Order with respect to the Hydroxide
To determine the order with respect to the hydroxide a second reaction of 10 mL of
0.0025 M Methylene Blue was reacted with 0.5 M NaOH, and the time-dependent
Absorbance at 598 nm was measured, and plotted as lnA vs time.
Table 2: Slope of the lnA vs. time graphs for the reaction of 0.0025M methylene blue with 0.1M and 0.5 M
NaOH
sample
M NaOH
V NaOH
(mL)
M MB+
V MB+
1
2
0.100M
0.500M
5 mL
5 mL
0.0025M
0.0025M
5 mL
5 mL
Slope of
Ln(A) vs t
graph
-0.0121
-0.0331
Sample Calculations
y
slope1 -k(T ) æ [0.05M ] ö
=
iç
= 0.2 y
÷
slope2 -k(T ) è [0.25M ] ø
-0.0121
= 0.366 = 0.2 y
-0.0331
y=
log ( 0.366 )
= 0.63
log ( 0.2 )
From these two trials the order with respect to the hydroxide y = 0.63. Further
trials would be needed to see how large the errors are in this measurement. (The
order can sometimes be fractional, but for this reaction it is more likely to be y=1
since then the reaction would be a simple one step reaction)
Part C: Determining the Collision Factor and the Activation Energy
Six reactions were conducted. In each reaction 10 mL of 0.1M NaOH was mixed with
10 mL of 0.0025M Methylene blue. In each case the reactants were equilibrated to
different temperatures in the range 275-320K. By monitoring the absorbance at
578 nm, and plotting lnA vs t, the rate constant for the reaction could be obtained as
follows
-slope
-slope
=
- 0.63
[OH ]o
0.05 0.63
k(T ) =
where y=0.63 is the order with respect to the hydroxide. By plotting ln(k) vs. 1/T,
lnA is obtained as the intercept and Ea = slope x R (R = molar gas constant = 8.314
J/(mol K))
Table 3: Measurement of k(T)
T(K)
276.4
281.8
286.5
306.5
297.3
320
slope
[OH] mol/L k
1/T
Ln(k)
-0.0003471
0.05 0.002291414 0.003617945 -6.078586303
-0.0001568
0.05 0.00103513 0.003548616 -6.873228118
-0.0001614
0.05 0.001065497 0.003490401 -6.84431347
-0.002058
0.05 0.013586083 0.003262643 -4.298709309
-0.001746
0.05 0.011526385 0.003363606 -4.463116489
-0.003483
0.05 0.022993356
0.003125 -3.772549955
From the Arhenius plot the activation energy for the reaction is
Ea = 58.15 ± 28.87kJ / mole at the 95% confidence level while the activation energy
lies in the range 5.16E4-7.06E9 at the 65% confidence level, with a mean value of A
= 1.91E7
0
0.0031 0.0032 0.0033 0.0034 0.0035 0.0036 0.0037
-1
-2
y = -6513x + 16.765
R² = 0.7787
ln(k)
-3
-4
-5
Series1
-6
Linear (Series1)
-7
-8
1/T (K-1)
Figure 6: Arrhenius plot for the reaction of 0.00125 M Methylene blue and 0.05M sodium hydroxide
Conclusion: The rate law for the reaction of methylene blue with sodium hydroxide
has been determined. It is found to be
rate = Ae- Ea /RT [MB + ][OH - ]0.63
where
A = 5.16 ´ 10 4 - 7.06 ´ 10 9
Ea = 58.15 ± 28.87kJ / mole
The order with respect to the hydroxide should be treated with caution, as it is
based on only one trial and no value for the standard deviation in this value is know.
Additional trials should be undertaken to see if the order is truly fractional or
integer. If integer then the reaction would be first order in hydroxide and second
order overall. The overall reaction
MB+ (aq) + OH - (aq) ® MBOH (aq)
could occur in one elementary step which is most likely for such a simple reaction.
The most likely form of error is in the pipetting of the reactants. More trials would
help to reduce the errors.