1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
riadik2000 [5.3K]
2 years ago
7

A certain first-order reaction has a half-life of 25.2 s at 20°C. What is the value of the rate constant k at 60°C if the activa

tion energy, Ea=80 kJ mol-1?
Chemistry
1 answer:
DochEvi [55]2 years ago
3 0

Answer:

t

(

2

)

1/2

=

85.25 s

Notice how you're given the half-life (for one temperature), a second temperature, and the activation energy. The key to doing this problem is recognizing that:

the half-life for a first-order reaction is related to its rate constant.

the rate constant changes at different temperatures.

Go here for a derivation of the half-life of a first-order reaction. You should find that:

t

1/2

=

ln

2

k

Therefore, if we label each rate constant, we have:

k

1

=

ln

2

t

(

1

)

1/2

k

2

=

ln

2

t

(

2

)

1/2

Recall that the activation energy can be found in the Arrhenius equation:

k

=

A

e

−

E

a

/

R

T

where:

A

is the frequency factor, i.e. it is proportional to the number of collisions occurring over time.

E

a

is the activation energy in

kJ/mol

.

R

=

0.008314472 kJ/mol

⋅

K

is the universal gas constant. Make sure you get the units correct on this!

T

is the temperature in

K

(not

∘

C

).

Now, we can derive the Arrhenius equation in its two-point form. Given:

k

2

=

A

e

−

E

a

/

R

T

2

k

1

=

A

e

−

E

a

/

R

T

1

we can divide these:

k

2

k

1

=

e

−

E

a

/

R

T

2

e

−

E

a

/

R

T

1

Take the

ln

of both sides:

ln

(

k

2

k

1

)

=

ln

(

e

−

E

a

/

R

T

2

e

−

E

a

/

R

T

1

)

=

ln

(

e

−

E

a

/

R

T

2

)

−

ln

(

e

−

E

a

/

R

T

1

)

=

−

E

a

R

T

2

−

(

−

E

a

R

T

1

)

=

−

E

a

R

[

1

T

2

−

1

T

1

]

Now if we plug in the rate constants in terms of the half-lives, we have:

ln

⎛

⎜

⎝

ln

2

/

t

(

2

)

1/2

ln

2

/

t

(

1

)

1/2

⎞

⎟

⎠

=

−

E

a

R

[

1

T

2

−

1

T

1

]

This gives us a new expression relating the half-lives to the temperature:

⇒

ln

⎛

⎜

⎝

t

(

1

)

1/2

t

(

2

)

1/2

⎞

⎟

⎠

=

−

E

a

R

[

1

T

2

−

1

T

1

]

Now, we can solve for the new half-life,

t

(

2

)

1/2

, at the new temperature,

40

∘

C

. First, convert the temperatures to

K

:

T

1

=

25

+

273.15

=

298.15 K

T

2

=

40

+

273.15

=

313.15 K

Finally, plug in and solve. We should recall that

ln

(

a

b

)

=

−

ln

(

b

a

)

, so the negative cancels out if we flip the

ln

argument.

⇒

ln

⎛

⎜

⎝

t

(

2

)

1/2

t

(

1

)

1/2

⎞

⎟

⎠

=

E

a

R

[

1

T

2

−

1

T

1

]

⇒

ln

⎛

⎜

⎝

t

(

2

)

1/2

400 s

⎞

⎟

⎠

=

80 kJ/mol

0.008314472 kJ/mol

⋅

K

[

1

313.15 K

−

1

298.15 K

]

=

(

9621.78 K

)

(

−

1.607

×

10

−

4

K

−

1

)

=

−

1.546

Now, exponentiate both sides to get:

t

(

2

)

1/2

400 s

=

e

−

1.546

⇒

t

(

2

)

1/2

=

(

400 s

)

(

e

−

1.546

)

=

85.25 s

This should make sense, physically. From the Arrhenius equation, the higher

T

2

is, the more negative the

[

1

T

2

−

1

T

1

]

term, which means the larger the right hand side of the equation is.

The larger the right hand side gets, the larger

k

2

is, relative to

k

1

(i.e. if

ln

(

k

2

k

1

)

is very large,

k

2

>>

k

1

). Therefore, higher temperatures means larger rate constants.

Furthermore, the rate constant is proportional to the rate of reaction

r

(

t

)

in the rate law. Therefore...

The higher the rate constant, the faster the reaction, and thus the shorter its half-life should be.

Explanation:

Sorry just go here https://socratic.org/questions/588d14f211ef6b4912374c92#370588

You might be interested in
2. What physical force causes suspensions to settle
MakcuM [25]

Hello!

Answer:

Gravity

Explanation:

It can settle down and separate over time due to gravity.

Hope this helps! Have a great day!

8 0
2 years ago
What decomposers are in a estuary ?
belka [17]
They are <span>Common Soil </span><em>Bacteria</em><span> Nematodes.

                                  Hope this helps:)</span>
7 0
3 years ago
I AM GIVING BRAINLIEST PLEASEE HELPPPP I NEED HELPPPPPP PLEAEEEEEE
True [87]

Answer:

0.479 M or mol/L

Explanation:

So Molarity is moles/litres of solution...often written as M=mol/L

So here we are given grams of BaCl2 which we have to convert to moles. To convert to moles of BaCl2 we have to divide 63.2 g BaCl2 by molar mass of BaCl2 which is 208.23 g/mol so you get 63.2/208.23 = 0.3035 moles of BaCl2

Second step is converting the 634mL to litres by simply dividing by 1000 because we know 1 litre has 1000ml so 634/1000 = 0.634L

Now we just plug these guys in our molarity formula M=mol/L

M= 0.3035/0.634 = 0.479 M or mol/L

3 0
3 years ago
Read 2 more answers
An alloy of bronze is manufactured by melting 51.2 g of copper with 6.84 g of tin. What is the percent copper in the bronze?
Harlamova29_29 [7]

Answer:

Percentage of copper = 88%

Explanation:

Given data:

Mass of copper = 51.2 g

Mass of tin = 6.84 g

Percentage of copper = ?

Solution:

Formula:

Percentage of copper = mass of copper / total mass × 100

Now we will determine the total mass:

Total mass = mass of copper + mass of  tin

Total mass = 51.2 g + 6.84 g

Total mass = 58.04 g

Now we will calculate the percentage of copper.

Percentage of copper = 51.2 g / 58.04 g × 100

Percentage of copper = 0.88 × 100

Percentage of copper = 88%

5 0
3 years ago
How are genes and alleles related
Montano1993 [528]
Alleles are inside a gene and genes are made up by alleles. Also, a gene is DNA, so the allele is like piece of DNA inside a gene<span>.

Hope this helps:)
</span>
7 0
3 years ago
Other questions:
  • One reaction that destroys o3 molecules in the stratosphere is
    10·1 answer
  • Select the false statement below concerning period 4 transition elements. A. The nickel atom has 18 inner/core electrons. B. Bot
    10·1 answer
  • Change 32L of carbon dioxide into moles of carbon dioxide
    6·1 answer
  • Refer to the first three rows of the periodic table, what element has properties most similar to carbon?
    9·1 answer
  • If an element has 12 protons and 17 neutrons, how many electrons must it have?
    5·2 answers
  • BaCI2+Na2CO3 need help
    9·1 answer
  • Does anyone know how to do this?
    12·1 answer
  • Y
    15·1 answer
  • Calcula el pH de las siguientes sustancias formadas durante una erupción volcánica:
    12·1 answer
  • What is the pH of the solution if the [H+] is 1 x 10-12 ?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!