a first order reaction is 50% complete in 30.2 minutes has a a half life period is
please slove this question in detail
Answers
hey the answer is given in the question only.50% in fact means half so half of the reaction is cmpletd in 30.2mins and it is in fact called the half life period of reaction as half life period of reaction is the time taken to cmplete half of the reaction.
Answer:
100 min
Explanation:
The integrated rate law for a first-order reaction looks like this
ln
(
A
A
0
)
=
−
k
⋅
t
, where#
A
- the concentration at a given time
t
A
0
- the initial concentration
k
- the rate constant, usually expressed in
s
−
1
for first-order reactions
Now, I'll assume that you're not familiar with the equation that describes the half-life of a first-order reaction.
As you know, the half-life of a chemical reaction tells you how much time is needed for the concentration of a reactant to reach half of its initial value.
Simply put, the time needed for
50
%
of a reaction to be completed will represent that reaction's half-life.
In your case, you know that your first-order reaction is
50
%
completed after
30
minutes. This means that after
30
minutes, you will have
A
=
1
2
⋅
A
0
→
half of the initial concentration remains after one half-life
Plug this into the above equation and solve for
k
, the rate constant
ln
(
1
2
⋅
A
0
A
0
)
=
−
k
⋅
30 min
This is equivalent to
−
k
⋅
30 min
=
ln
(
1
2
)
−
k
⋅
30 min
=
=
0
ln
(
1
)
−
ln
(
2
)
k
=
ln
(
2
)
30 min
=
2.31
⋅
10
−
2
min
−
1
Now that you know the rate constant for this reaction, use the same equation again, only this time use
A
=
1
10
⋅
A
0
→
equivalent to
90
%
completion
and solve for
t
, the time needed to get here
ln
(
1
10
⋅
A
0
A
0
)
=
−
2.31
⋅
10
−
2
min
−
1
⋅
t
This is equivalent to
t
=
−
ln
(
10
)
−
2.31
⋅
10
−
2
min
−
1
=
99.68 min
Rounded to one sig fig, the answer will be
t
=
100 min
