2. THERMODYNAMICS OF LlVHSfG SYSTEMS
61
fremely limited. Ordinary plants and animals carry out normal life
activities only over the approximate range of 0-50°. Some organisms
are, of course, less sensitive. Some thermophilic algae and bacteria live
in hot springs at temperatures up to 70° or perhaps even higher. Mammals, on the other hand, are very sensitive to body temperatures only
a few degrees higher than normal. In the other direction, almost all organisms are inactive as temperatures of 0° are approached, although
some plants continue to grow slowly even at several degrees below
this.
Biologists often express the effect of temperature on the rate of a
reaction in terms of the temperature coefficient or C/'io·
This is the ratio
between the rate of a reaction at one temperature and its rate at a
temperature 10° lower as given by the equation
Qio = ^ψ
(126)
where k is the rate constant and t is temperature. A more useful expression is given by the van't Hoff equation
or
i n
10 , fa
log <*»-ü=Ti
l0g
h
where k x and k 2 are the reaction rates at temperatures t x and t 2 , respectively. The Q 10 for most biological processes is approximately 2. The
value of Q 10 will vary somewhat with temperature, therefore the temperature over which Q 10 has been measured should always be given.
Temperature, then, is a very important factor in determining the
rate of a reaction. The question immediately arises as to the mechanism
involved. As temperature increases, the kinetic energy of molecules is
increased. However, the small increase in the average molecular kinetic
energy cannot account for the observed increase in reaction rate. Arrhenius proposed that the rate of a reaction is controlled, not by the
average kinetic energy of the reacting molecules, but by the concentration of molecules possessing more than a critical amount of energy (the
so-called energy of activation). The effect of temperature on the increase in concentration of molecules with the proper energy of activation is similar to the effect of temperature on the rate of reaction.
Arrhenius found a linear relation between the rate constant for a reaction and the reciprocal of the absolute temperature. This led to the
61
fremely limited. Ordinary plants and animals carry out normal life
activities only over the approximate range of 0-50°. Some organisms
are, of course, less sensitive. Some thermophilic algae and bacteria live
in hot springs at temperatures up to 70° or perhaps even higher. Mammals, on the other hand, are very sensitive to body temperatures only
a few degrees higher than normal. In the other direction, almost all organisms are inactive as temperatures of 0° are approached, although
some plants continue to grow slowly even at several degrees below
this.
Biologists often express the effect of temperature on the rate of a
reaction in terms of the temperature coefficient or C/'io·
This is the ratio
between the rate of a reaction at one temperature and its rate at a
temperature 10° lower as given by the equation
Qio = ^ψ
(126)
where k is the rate constant and t is temperature. A more useful expression is given by the van't Hoff equation
or
i n
10 , fa
log <*»-ü=Ti
l0g
h
where k x and k 2 are the reaction rates at temperatures t x and t 2 , respectively. The Q 10 for most biological processes is approximately 2. The
value of Q 10 will vary somewhat with temperature, therefore the temperature over which Q 10 has been measured should always be given.
Temperature, then, is a very important factor in determining the
rate of a reaction. The question immediately arises as to the mechanism
involved. As temperature increases, the kinetic energy of molecules is
increased. However, the small increase in the average molecular kinetic
energy cannot account for the observed increase in reaction rate. Arrhenius proposed that the rate of a reaction is controlled, not by the
average kinetic energy of the reacting molecules, but by the concentration of molecules possessing more than a critical amount of energy (the
so-called energy of activation). The effect of temperature on the increase in concentration of molecules with the proper energy of activation is similar to the effect of temperature on the rate of reaction.
Arrhenius found a linear relation between the rate constant for a reaction and the reciprocal of the absolute temperature. This led to the