Transcript File

Rates and orders of reactions
Rate Constant
• The order of a reaction refers to the way in
which the concentration of drug or reactants
influences the rate of a chemical reaction or
process.
– Zero-Order Reactions
– First-Order Reactions
Zero-Order Reactions
• a graph of A versus t yields a straight line.
– The y intercept is equal to A0
– The slope of the line is equal to k0.
• Equation above may be expressed
in terms of drug concentration,
which can be measured directly.
C  k0t C 0
A  k0t  A0
– C 0 is the drug concentration at time 0
– C is the drug concentration at time t.
– k 0 is the zero-order decomposition constant.
First-Order Reactions
• Equation may also be expressed as:
A  A0 e
 kt
• Because ln = 2.3 log, Equation becomes:
 kt
log A 
 log A0
2.303
First-Order Reactions
• When drug decomposition involves a solution, starting with
initial concentration C 0, it is often convenient to express the
rate of change in drug decomposition, dC/dt, in terms of drug
concentration, C, rather than amount because drug
concentration is assayed. Hence,
ln C  kt  ln C0
 kt
log C 
 log C0
2.3
First-Order Reactions
• a graph of log A versus t
will yield a straight line .
• The y intercept will be
log A0
• The slope of the line will be
–k/2.3 .
• Similarly, a graph of log C
versus t will yield a straight
line. The y intercept will be
log C 0, and the slope of the
line will be –k/2.3.
First-Order Reactions
• C versus t may be plotted on semilog paper
without the need to convert C to log C. An
example is shown:
Half-Life
• Half-life (t 1/2) expresses the period of time
required for the amount or concentration of a
drug to decrease by one-half.
Zero-Order Half-Life
• The t1/2 for a zero-order process is not
constant. The zero-order t1/2 is proportional to
the initial amount or concentration of the
drug and is inversely proportional to the zeroorder rate constant k0:
t1 / 2
0.5 A0

k0
First-Order Half-Life
• The t 1/2 for a first-order reaction may be
found by means of the following equation:
t1/ 2
0.693

k
• t 1/2 is a constant. No matter what the initial
amount or concentration of drug is, the time
required for the amount to decrease by onehalf is a constant.
Example
• A pharmacist weighs exactly
10 g of a drug and dissolves it
in 100 mL of water. The
solution is kept at room
temperature, and samples are
removed periodically and
assayed for the drug. The
pharmacist
obtains
the
following data:
Time (hr)
Drug Conc.
(mg/mL)
0
100
2
95
4
90
6
85
8
80
10
75
12
70
• From these data, a graph constructed by plotting the
concentration of drug versus time will yield a straight line.
Therefore, the rate of decline in drug concentration is of zero
order.
• The zero-order rate constant k 0 may be obtained from the
slope of the line or by proper substitution into Equation .
C  k0t C 0
• If
Co=conc. Of 100mg/ml at t = 0
• And C = conc. Of 90mg/ml at t = 4hr
• Then 90 = -k0 (4) + 100
K0 = 2.5mg/ml hr
Example 1
• A pharmacist dissolves
exactly 10 g of a drug
into 100 mL of water.
The solution is kept at
room temperature, and
samples are removed
periodically and assayed
for the drug. The
pharmacist obtains the
following data:
Time (hr)
Drug Conc. Log Drug
(mg/mL) Conc.
0
100.00
2.00
4
50.00
1.70
8
25.00
1.40
12
12.50
1.10
16
6.25
0.80
20
3.13
0.50
24
1.56
0.20
• The relationship of time versus drug concentration in
indicates a first-order reaction.
• The t1/2 for a first-order process is constant and may
be obtained from any two points on the graph that
show a 50% decline in drug concentration.
• In this example, the t 1/2 is 4 hours. The first-order
rate constant may be found by:
1) obtaining the product of 2.3 times the slope.
2) by dividing 0.693 by the t 1/2, as follows:
Example 2
• Plot the following data on both
semilog graph paper and standard
rectangular coordinates.
a. Does the decrease in the amount
of drug A appear to be a zeroorder or a first-order process?
b. What is the rate constant k?
c. What is the half-life t 1/2?
d. Does the amount of drug A
extrapolate to zero on the x axis?
e. What is the equation for the line
produced on the graph?
Time (min) Drug A (mg)
10
96.0
20
89.0
40
73.0
60
57.0
90
34.0
120
10.0
130
2.5
a. Zero-order process .
b. Rate constant, k 0:
Example 3
Plot the following data on both semilog
graph paper and standard rectangular
coordinates.
Answer questions a, b, c, d, and e as
stated in Question 1.
Time
(min)
4
Drug A
(mg)
70.0
10
58.0
20
42.0
30
31.0
60
12.0
90
4.5
120
1.7
a. First-order process.
b. Rate constant, k:
Homework
• A pharmacist dissolved a few
milligrams of a new antibiotic
drug into exactly 100 mL of
distilled water and placed the
solution in a refrigerator (5°C). At
various time intervals, the
pharmacist removed a 10-mL
aliquot from the solution and
measured the amount of drug
contained in each aliquot. The
following data were obtained.
Time (hr)
0.5
Antibiotic
(g/mL)
84.5
1.0
81.2
2.0
74.5
4.0
61.0
6.0
48.0
8.0
35.0
12.0
8.7
a. Is the decomposition of this antibiotic a firstorder or a zero-order process?
b. What is the rate of decomposition of this
antibiotic?
c. How many milligrams of antibiotics were in
the original solution prepared by the
pharmacist?
d. Give the equation for the line that best fits
the experimental data.