PR-2: Pemodelan Kualitas Air Permukaan Agnes Ferinna-0906551451-Teknik Sipil 2.1.
You perform a series of of batch experiments and come up with the following data: t (hour) c (μ gram/Liter)
0 10,5
2 5,1
4 3,1
6 2,8
8 2,2
10 1,9
Determine the order (n) and the rate (k) of the underlying reaction. Answer: Zero-Order
x = t (hour) y = c (μ (μ gram/Liter ) Figure 1. Plot of concentration versus time for a zero-order reaction
Zero-Order 12 10 ) r e t i 8 l / m 6 a r g µ 4 ( c 2
y = -0,7429x + 7,981
Zero-Order Linear (Zero-Order)
0 0
5
10
15
t (hour)
First-Order
x = t (hour) y = ln c
Figure 2. Plot of concentration versus time for a first-order reaction
First-Order 2,500 2,000
y = -0,1596x + 2,06
c 1,500 n l
1,000
First-Order
0,500
Linear (First-Order)
0,000 0
5
10 t (hour)
15
Second-Order
x = t (hour) y = 1/c
Figure 3. Plot of concentration versus time for a second-order reaction
Second-Order 0,600 0,500 y = 0,0424x + 0,1135
0,400 c / 0,300 1
Second-Order
0,200
Linear (Second-Order)
0,100 0,000 0
5
10
15
t (hour)
Dari ketiga plot reaksi diatas (zero-order, first-order dan second-order) didapat gambaran hubungan sebaran data terhadap garis regresinya per masing-masing orde reaksi, dimana pada akhirnya orde reaksi yang dipilih adalah berdasarkan plot garis regresi yang paling mewakili sebaran data tersebut. Dari ketiga plot diatas didapat bahwa garis regresi yang paling mewakili plot sebaran data adalah pada saat plot reaksi second-order dimana persamaan dasarnya adalah 1/c = 1/c0 + kt. Sehingga dapat dianalisis nilai laju reaksi (k), yakni sebagai berikut:
y = 0,0424x + 0,1135 Maka laju reaksi/k = 0,0424 dan orde reaksi/n = 2 , karena merupakan reaksi Second-Order.
2.6.
You set up a series of 300 mL bottles and add 10 mL of a glucose solution to each. Note that the glucose solution has a concentration of 100 mgCL-1. To each bottle you add a small quantity (that is, with an insignificant amount of carbon compared to the glucose) of bacteria. You fill the remainder of their volumes up with water. Finally you seal each bottle and incubate them at 20°C. At various times you open one of the bottles and measure its oxygen content. The following data results: 0
t (day) -1
c (mgO2L )
2
5
10
20
30
40
50
60
70
10 8,4 6,5 4,4 2,3 1,6 1,3 1,2 1,1 1,1
a. Develop a conceptual model for what is taking place inside the bottle. b. Using the information from this lecture, attempt to estimate the decay rate for the glucose. Answer: [Glukosa]awal = 100 mgC.L -1 = 100 gramC.m -3 dalam satuan karbon Pengenceran larutan glukosa: [Glukosa]awal = 100 gramC/m 3 Volume glukosa = 10 mL Volume botol = 300 mL
Volume air = volume botol – volume glukosa Volume air = 300 mL – 10 mL = 290 mL
] [] [ [] C6H12O6 + 6O2 6CO2 + 6 H2O r oc = massa oksigen yang dikonsumsi untuk setiap karbon yang terdekomposisi
r oc = 2,67 gramO.gramC -1
Zero-Order
x = t (day) y = c (mgO2/Liter)
Figure 1. Plot of concentration versus time for a zero-order reaction
Zero-Order Glucose Decomposition 12 10 y = -0,1114x + 6,9881
8
Zero-Order Glucose Decomposition
) 1 L 2 6 O g m 4 ( c
Linear (Zero-Order Glucose Decomposition)
2 0 0
-2
20
40
60
80
t (day)
First-Order
x = t (day) y = ln c
Figure 2. Plot of concentration versus time for a first-order reaction
First-Order Glucose Decomposition 2,5 y = -0,0324x + 1,903
2 1,5 c n l
First-Order Glucose Decomposition
1 0,5 0 -0,5
0
-1
Second-Order
x = t (hour) y = 1/c
20
40
t (day)
60
80
Linear (First-Order Glucose Decomposition)
Figure 3. Plot of concentration versus time for a second-order reaction
Second-Order Glucose Decomposition 1,2 y = 0,013x + 0,1338
1 0,8 c / 0,6 1
Second-Order Glucose Decomposition
0,4
Linear (Second-Order Glucose Decomposition)
0,2 0 0
20
40
60
80
t (day)
Dari ketiga plot reaksi diatas (zero-order, first-order dan second-order) didapat gambaran hubungan sebaran data terhadap garis regresinya per masing-masing orde reaksi, dimana pada akhirnya orde reaksi yang dipilih adalah berdasarkan plot garis regresi yang paling mewakili sebaran data tersebut. Dari ketiga plot diatas didapat bahwa garis regresi yang paling mewakili plot sebaran data adalah pada saat plot reaksi second-order dimana persamaan dasarnya adalah 1/c = 1/c0 + kt. Sehingga dapat dianalisis nilai laju reaksi (k), yakni sebagai berikut:
y = 0,013x + 0,1338 Maka laju reaksi/k = 0,013 dan orde reaksi/n = 2, karena merupakan reaksi SecondOrder. Decay rate glukosa menurut reaksi Second-Order:
[]
2.17.
The following data for concentrations and times were developed for a series of batch experiments having different initial conditions: t 0 1 2
c
1 2 5 10 0,95 1,87 4,48 8,59 0,91 1,74 4,04 7,46
Assuming that Eq. 2.7. holds, use the method of initial rates to determine the order and the rate of the reaction. Answer:
( ) x = log c0 y = log
Figure 1. Plot of log
versus log c
0
Method of Initial Rates 1,6 1,4 1,2 y = 1,3081x - 0,1265
1
) t d 0,8 / 0 c 0,6 d ( g 0,4 o l
Method of Initial Rates Linear (Method of Initial Rates)
0,2 0
-0,2 0
0,2
0,4
-0,4
0,6
0,8
1
1,2
log c0
Dari plot diatas didapat bahwa persamaan sebaran datanya adalah log
=
1,3081 log c 0 – 0,1265. Sehingga dapat dianalisis nilai laju reaksi (k), yakni sebagai berikut:
( ) y = 1,3081x – 0,1265
k = log-1 (-0,1265) = 0,7473 Maka laju reaksi/k = 0,7473 dan orde reaksi/n = 1,3081 .
2.18.
Assuming that Eq. 2.7. holds, use the method of half-lives to determine the reaction order and rate by evaluating the following half-lives and initial concentrations developed from a series of batch experiments: c0
1
2
5
10
t50
16
11
7
5
Answer:
x = log c0 y = log t 50
Figure 1. Plot of log t 50 versus log c0
Method of Half-Lives 1,400 1,200 1,000 y = -0,5035x + 1,1992
0,800
0 5
t g o 0,600 l
Method of Half-Lives Linear (Method of Half-Lives)
0,400 0,200 0,000 0
0,2
0,4
0,6
0,8
1
1,2
log c0
Dari plot diatas didapat bahwa persamaan sebaran datanya adalah log t 50 = -0,5035 log c0 + 1,1992. Sehingga dapat dianalisis nilai laju reaksi (k), yakni sebagai berikut:
( ) y = -0,5035x + 1,1992
k = log-1 (1,1992) = 15,82 Maka laju reaksi/k = 15,82 dan orde reaksi/n = -0,5035 .
