MANICALAND STATE UNIVERSITY OF APPLIED SCIENCE

FACULTY OF ENGINEERING

NAMES : CHINGANGU OSCAR T

REG NUMBER : M22BMZ
LEVEL : 3.1
MODULE : SEPARATION PROCESSES
MODULE CODE : CHEP 315
TASK : ALTERNATIVE TO PRACTICAL ASSIGNMENT
PROGRAMME : CHEMICAL ENGINEERING
YEAR : 2025

Table 1: 15°C
 Mean Cₑ
C₀(mg/L) (mg/L) qₑ (mg/g) Cₑ/qₑ ln Cₑ ln qₑ

50 0 50 0 0 3.91

100 0 100 0 0 4.6

150 0 150 0 0 5.01

200 0 200 0 0 5.3

225 8.650 216.350 0.040 2.158 5.38

250 19.720 230.280 0.086 2.982 5.44

300 51.530 248.470 0.207 3.942 5.52

350 73.170 276.830 0.264 4.293 5.62

400 112.010 287.990 0.389 4.719 5.66

450 154.960 295.040 0.525 5.043 5.69

Table 2: 25°C
Mean Cₑ
C₀(mg/L) (mg/L) qₑ (mg/g) Cₑ/qₑ ln Cₑ ln qₑ

50 0 50 0 0 3.91

100 0 100 0 0 4.61

150 0 150 0 0 5.01

200 0.0280 199.9720 0.0001 -3.5756 5.3

225 0.0760 224.9240 0.0003 -2.5770 5.42

250 1.8200 248.1800 0.0070 0.5989 5.51

300 17.9100 282.0900 0.0634 2.8853 5.64

350 44.7300 305.2700 0.1465 3.8006 5.72

400 82.9300 317.0700 0.2616 4.4180 5.76

450 124.1400 325.8600 0.3810 4.8214 5.79

Table 3: 35°C
Mean Cₑ
C₀(mg/L) (mg/L) qₑ (mg/g) Cₑ/qₑ ln Cₑ ln qₑ

50 0 50 0 0 3.91

100 0 100 0 0 4.61

150 0 150 0 0 5.01

200 0 200 0 0 5.3

225 0 225 0 0 5.42

250 0 250 0 0 5.52

300 0.2500 299.7500 0.0008 -1.3863 5.70

350 9.6000 340.4000 0.0282 2.2618 5.83

400 39.4000 360.6000 0.1093 3.6738 5.89

450 87.2900 362.7100 0.2407 4.4692 5.89

Table 4: 45°C
Mean Cₑ
C₀(mg/L) (mg/L) qₑ (mg/g) Cₑ/qₑ ln Cₑ ln qₑ

50 0 50 0 0 3.91

100 0 100 0 0 4.61

150 0 150 0 0 5.01

200 0 200 0 0 5.3

225 0 225 0 0 5.42

250 0 250 0 0 5.52

300 0.1200 299.8800 0.0004 -2.1203 5.71

350 0.9700 349.0300 0.0028 -0.0305 5.86

400 6.4300 393.5700 0.0163 1.8610 5.9

450 35.5100 414.4900 0.0857 3.5698 6.027

ii)Blue =15 degrees, Orange =25 degrees, Grey =35 degrees, Yellow =45 degrees

0.6 linearized langmuir isotherm

f(x) = 0.00341479578076681 x + 0.00771226674326064

0.5 R² = 0.996559865360545

0.4
f(x) = 0.00309366942950167 x + 0.00199941243192277
R² = 0.999218009711559
0.3
Cₑ/qₑ

f(x) = 0.00275802240203436 x + 0.000237868812013993

0.2 R² = 0.999950361943969

0.1
f(x) = 0.00241244977485383 x + 0.000138075251324967
R² = 0.999893058195184
0
0 20 40 60 80 100 120 140 160 180
Mean Cₑ (mg/L)

langmuir non-linearlized

450

400

350

300

250
qₑ (mg/g)

200

150

100

50

0
0 20 40 60 80 100 120 140 160 180

Mean Cₑ (mg/L)
 Freundlich linear adsorpti on graph
6.2

6
f(x) = 0.0590014816530629 x + 5.84411780943257
R² = 0.969590619631061
f(x) = 0.0342677157067738
5.8 x + 5.75023940452109
R² = 0.984041469510996
f(x) = 0.0542841150079539 x + 5.51006474474675
R² = 0.976782269770563 5.6 f(x) = 0.0803283438725544 x + 5.25021880991141
R² = 0.91101789723051
Inqe

5.4

5.2

4.8
-4 -3 -2 -1 0 1 2 3 4 5 6
InCe

iii) Using the linearised graphs from (ii) for the calculation of this table

Ce/qe = [1/b*qe] + [Ce/qm] that is the linear Langmuir equation

Qe = (Ce*b*qm)/(1+ Ce*b) that is the non linear Langmuir adsorption equation

Inqe = InKf + (1/n)InCe that is the liear freundlich adsorption equation

RL (separation factor) =1/(1+KL*Co) where KL = b is the Langmuir constant and Co

is the initial concentration of metal

Isotherm Temperature ( °C)

model 15 25 35 45
Langmuir
Linear
qm (mg g-1) 294.12 322.58 357.14 384.62
b (L mg-1) 0.442 1.409 7 86.66
RL 0.323 0.0139 2.849E-3 2.307E-4
R2 0.9966 0.999 0.998 0.99973

Freundlich
Linear
Kf (mg g-1) 190.60 247.18 314.25 345.19
 1/n 0.0803 0.0543 0.0343 0.059
R2 0.911 0.9768 0.984 0.9696

iv) The mode that best describes the adoption is the Langmuir model. This is because R 2
value for all the Langmuir linearised graphs is 0.99 which is approximately equal to 1.

T 1/T Kc Inkc
228.15 0.004383 3728712 15.13157
298.15 0.003354 11886324 16.2909
308.15 0.003245 59052000 17.89393
318.15 0.003143 73106376 20.41001
0

Kc = Mw(hexavalent chromium molecular mass)*55.5*1000*KL. Where KL is b

vant hoff plot

25

20
f(x) = − 3077.57993276812 x + 28.299647385938
15 R² = 0.597843446497062
In Kc

10

0
0.003 0.0032 0.0034 0.0036 0.0038 0.004 0.0042 0.0044 0.0046
1/T (1/Kelvin

Using the equation from the Vant hoff plot; y=3077.6+28.3

And ∆G°= -RTInKc

 Temperature (°C) ∆G° (kJ mol-1) ∆H° (kJ mol-1 ) ∆S° (kJ mol-1 K-1)
15 -28.70215 +25.5871 +0.2353
25 -40.382194 +25.5871 +0.2353
35 -45.84352 +25.5871 +0.2353
45 -53.9865 +25.5871 +0.2353

(ii) Comment on the value of ∆G°, ∆H° and ∆S°

∆H° - is constant because it is undergoing the same reaction.
∆S° -is constant because the reaction is adiabatic and reversible.
∆G°- as temperature increases the rate of reaction increases hence free energy is decreasing
so that the reaction can proceed.
Time, Co Mean Ce t/qt qe-qt ln(qe-qt)
t (min) (mg/L) (mg/L) Co −Ct (min.g.mg-1) (mg/g)
q t=( )V
m
(mg/g)
1 50 23.89 26.11 0.0383 23.89 3.17
2 50 21.75 28.25 0.0708 21.75 3.08
3 50 18.10 31.90 0.0940 18.10 2.90
4 50 18.92 31.08 0.1287 18.92 2.94
5 50 16.56 33.44 0.1495 16.56 2.81
10 50 13.60 36.40 0.2747 13.6 2.61
15 50 9.82 40.18 0.3733 9.82 2.24
20 50 8.77 41.23 0.4851 8.77 2.17
30 50 6.36 43.64 0.6874 6.36 1.85
45 50 4.42 45.58 0.9873 4.42 1.49
60 50 0.99 49.01 1.2242 0.99 -0.01
90 50 0.52 49.49 1.8185 0.51 -0.67
120 50 0.24 49.76 2.4116 0.24 -1.43
150 50 0.094 49.91 3.0054 0.09 -2.41
180 50 0.0081 49.9919 3.6007 0.01 -4.61
240 50 0.00 50.00 4.8000 0 -
300 50 0.00 50.00 6.0000 0 -
Table 8: Co = 100 mg/L:
Time, t Co Mean Ce t/qt qe-qt ln(qe-qt)
(min) (mg/L) (mg/L) Co −Ct (min.g.mg-1) (mg/g)
q t=( )V
m
(mg/g)
1 100 84.63 15.37 0.0651 84.63 4.44
2 100 70.34 29.66 0.0674 70.34 4.25
3 100 50.51 49.49 0.0606 50.51 3.92
4 100 48.08 51.92 0.0770 48.08 3.87
5 100 47.53 52.47 0.0953 47.53 3.86
10 100 32.74 67.26 0.1487 32.74 3.49
15 100 31.81 68.19 0.2200 31.81 3.46
20 100 25.57 74.43 0.2687 25.57 3.24
30 100 20.79 79.21 0.3787 20.79 3.03
45 100 18.50 81.50 0.5521 18.5 2.92
 60 100 12.07 87.93 0.6823 12.07 2.49
90 100 6.33 93.67 0.9608 6.33 1.85
120 100 0.034 99.97 1.2004 0.03 -3.51
150 100 0.0056 99.99 1.5001 0.01 -4.61
180 100 0.00 100 1.8000 - -
240 100 0.00 100 2.4000 - -
300 100 0.00 100 3.0000 - -

Table 9: Co = 150 mg/L:

Time, t Co Mean Ce Co −Ct t/qt qe-qt ln(qe-qt)
q t=( )V
(min) (mg/L) (mg/L) m (min.g.mg-1) (mg/g)
(mg/g)

1 150 84.57 65.43 0.0153 84.57 4.44

2 150 62.70 87.30 0.0229 62.7 4.14
3 150 65.44 84.56 0.0355 65.44 4.18
4 150 57.79 92.21 0.0434 57.79 4.02
5 150 57.23 92.77 0.0538 57.23 4.04
10 150 48.68 101.32 0.0987 48.68 3.88
15 150 37.33 112.67 0.1331 37.33 3.62
20 150 35.78 114.22 0.1751 35.78 3.58
30 150 23.44 126.56 0.2370 23.44 3.15
45 150 21.32 128.68 0.3497 21.32 3.06
 60 150 16.43 133.51 0.4494 16.49 2.8
90 150 11.79 138.21 0.6512 11.79 2.47
120 150 8.24 141.76 0.8465 8.24 2.12
150 150 2.50 147.50 1.0169 2.5 0.92
180 150 1.40 148.60 1.2113 1.4 0.34
240 150 0.76 149.24 1.6081 0.76 -0.27
300 150 0.20 149.80 2.0027 0.2 -1.61

Blue line C0-50,Grey line C0-100 AND Orange line = C0-150

Pseudo fi rst order linear graph

6

4
f(x) = − 0.019106379865379 x + 4.07297848990342
R² ==0.985143475818248
f(x) − 0.0206022827041264 x + 3.46870061457419
R² = 0.501546505284391
2 f(x) = − 0.0172963125548727 x + 2.24604697102722
R² = 0.505334341978849
ln(qe-qt)

0
0 50 100 150 200 250 300 350

-2

-4

-6
Time, t (min)

Blue line Co50, Orange line Co100 and Grey Co150

 Pseudo-second order for linear graph
7

6
f(x) = 0.0197618942054434 x + 0.0560638169446885
R² = 0.999826833038416
5

4
t/qt

3
f(x) = 0.00975428519168862 x + 0.061205081211589
R² = 0.999280725108504
2
f(x) = 0.00660756657887035 x + 0.0309383889376648
R² = 0.999313446086054
1

0
0 50 100 150 200 250 300 350
Time, t (min)

Blue line Co50, Orange line Co100 and Grey line Co150

non linear pseudo second order

160

140

120

100

80
𝒒_𝒕

60

40

20

0
0 50 100 150 200 250 300 350

Time, t (min)
(iii) Using the linear plots copy and complete Table10
Table 10: Table of kinetic data
Kinetic models Initial concentration (mg/L)
50
100 150
Pseudo-first-order
Linear
k1(min-1) 0.0206 0.019 0.0173
qe (mg g-1) 32.0950 58.7329 9.4499
R2 0.5015 0.9851 0.5053
Pseudo-second-
order
Linear
k2(g m-1.min-1) 7.1176E-4 3.1081E-3 6.9882E-3
qe (mg g-1) 151.5152 102.0408 50.5051
R2 0.9993 0.9993 0.9998

Conclusion
Following this study, the adsorption of Cr (iv) ions from heavy metal effluent was
successfully modelled using adsorption isotherms and kinetics. The Langmuir and Freundlich
models were used to fit the adsorption data, with the Freundlich model generally providing a
better fit. Thermodynamics analyses revealed that the adsorption process is spontaneous and
endothermic. Kinetic studies indicated that the pseudo-second-order model better described
the adsorption kinetics compared to the pseudo-first-order. This indicates that the adsorption
process is likely controlled by chemical interactions at the surface of the adsorbent.