Adenosine triphosphate, ATP, is used as a free-energy source by biological cells. (See the essay on page 624.) ATP hydrolyzes in the presence of enzymes to give ADP: ATP ( a q ) + H 2 O ( l ) → ADP ( a q ) + H 2 PO 4 − ( a q ) ; Δ G ° = − 30.5 kJ/mol at 25 ° C Consider a hypothetical biochemical reaction of molecule A to give molecule B: A ( a q ) → B ( a q ) ; Δ G ° = + 15.0 kJ/mol at 25 ° C Calculate the ratio [B]/[A] at 25°C at equilibrium. Now consider this reaction “coupled” to the reaction for the hydrolysis of ATP: A ( a q ) + ATP ( a q ) + H 2 O ( l ) → B ( a q ) + ADP ( a q ) + H 2 PO 4 − ( a q ) If a cell maintains a high ratio of ATP to ADP and H 2 PO 4 − by continuously making ATP, the conversion of A to B can be made highly spontaneous. A characteristic value of this ratio is [ ATP ] [ ADP ] [ H 2 PO 4 − ] = 500 Calculate the ratio [B][A] in this case and compare it with the uncoupled reaction. Compared with the uncoupled reaction, how much larger is this ratio when coupled to the hydrolysis of ATP?
Adenosine triphosphate, ATP, is used as a free-energy source by biological cells. (See the essay on page 624.) ATP hydrolyzes in the presence of enzymes to give ADP: ATP ( a q ) + H 2 O ( l ) → ADP ( a q ) + H 2 PO 4 − ( a q ) ; Δ G ° = − 30.5 kJ/mol at 25 ° C Consider a hypothetical biochemical reaction of molecule A to give molecule B: A ( a q ) → B ( a q ) ; Δ G ° = + 15.0 kJ/mol at 25 ° C Calculate the ratio [B]/[A] at 25°C at equilibrium. Now consider this reaction “coupled” to the reaction for the hydrolysis of ATP: A ( a q ) + ATP ( a q ) + H 2 O ( l ) → B ( a q ) + ADP ( a q ) + H 2 PO 4 − ( a q ) If a cell maintains a high ratio of ATP to ADP and H 2 PO 4 − by continuously making ATP, the conversion of A to B can be made highly spontaneous. A characteristic value of this ratio is [ ATP ] [ ADP ] [ H 2 PO 4 − ] = 500 Calculate the ratio [B][A] in this case and compare it with the uncoupled reaction. Compared with the uncoupled reaction, how much larger is this ratio when coupled to the hydrolysis of ATP?
Solution Summary: The author explains the relationship between free energy change and equilibrium constant.
Adenosine triphosphate, ATP, is used as a free-energy source by biological cells. (See the essay on page 624.) ATP hydrolyzes in the presence of enzymes to give ADP:
ATP
(
a
q
)
+
H
2
O
(
l
)
→
ADP
(
a
q
)
+
H
2
PO
4
−
(
a
q
)
;
Δ
G
°
=
−
30.5
kJ/mol at 25
°
C
Consider a hypothetical biochemical reaction of molecule A to give molecule B:
A
(
a
q
)
→
B
(
a
q
)
;
Δ
G
°
=
+
15.0
kJ/mol at 25
°
C
Calculate the ratio [B]/[A] at 25°C at equilibrium.
Now consider this reaction “coupled” to the reaction for the hydrolysis of ATP:
A
(
a
q
)
+
ATP
(
a
q
)
+
H
2
O
(
l
)
→
B
(
a
q
)
+
ADP
(
a
q
)
+
H
2
PO
4
−
(
a
q
)
If a cell maintains a high ratio of ATP to ADP and H2PO4− by continuously making ATP, the conversion of A to B can be made highly spontaneous. A characteristic value of this ratio is
[
ATP
]
[
ADP
]
[
H
2
PO
4
−
]
=
500
Calculate the ratio [B][A] in this case and compare it with the uncoupled reaction. Compared with the uncoupled reaction, how much larger is this ratio when coupled to the hydrolysis of ATP?
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The Laws of Thermodynamics, Entropy, and Gibbs Free Energy; Author: Professor Dave Explains;https://www.youtube.com/watch?v=8N1BxHgsoOw;License: Standard YouTube License, CC-BY