When we increase the temperature of a reaction the Rate of product formation increases. From a thermodynamic view increasing the temperature increases the average kinetic energy of the reactant molecules. According to the Collisional Theory, this increases the impact energy upon collision which increases the probability that more molecules will exceed the Activation Energy producing more product at an increased rate. How is this accomplished if concentrations are not altered? According to the Rate Law the only thing that would affect the Rate other than concentrations of reactants is to affect the rate constant itself. Svante Arrhenius investigated the relationship between rate constant and temperature change. He found that when he plotted the natural ln of the rate constant against the reciprocal Kelvin Temperature (1 / T) that it resulted in a straight line with a negative slope. The slope is -Ea / R where Ea is the Activation Energy (minimum energy required for product formation) and R is the universal gas law constant (8.31 J/mol-K). This can be done graphically or using the slope-intercept formula that can always be applied to any linear relationship:
y = mx + b
ln k = -Ea/R(1/T) + b
ln k2 = -Ea / R [1 / T2] + b
ln k1 = -Ea / R [1 / T1] + b
ln k2- ln k1= (-Ea / R [1 / T2] + b) - (-Ea / R [1 / T1] + b)
ln (k2 / k1) = -Ea / R [1 / T2 - 1 / T1]
ln (k2 / k1) = Ea / R [1 / T1 - 1 / T2]
This relationship is called the Arrhenius equation. Just how much will a small change in temperature affect the Rate? If a reaction has an Activation Energy of 50 kJ/mole what effect on the Rate would a change of temperature from 20to 30oC?
1. Convert the two temperatures to Kelvin:
T1 = 20+ 273 = 293 K
T2 = 30+ 273 = 303 K
2. Plug in Activation Energy, T1,T2, and R = 8.31 J/mole-K into the Arrhenius Equation.
ln (k2/k1) = [(50000 J/mole)/(8.31 J/mole K)](1/ 300 K - 1 /310 K)
ln (k2/k1) = 0.647
k2/k1 = e0.647 = 1.91
Note that a 10 oC change in temperature results in an approximate doubling of the reaction rate which is known as the Q10 rule and it can be predicted to be the case in this reaction also.
An actively respiring yeast culture will be placed in water baths at different temperatures and the rate of their respiration measured using a manometer and recording how much the fluid moves from its initial position after a time interval of five minutes. This will indicate how much gas is produced by the respiring yeast every five minutes at different temperatures. The rate of respiration can therefore, be calculated from these observations for each temperature and then compared to identify any trends.
These are the variables which have been controlled for this experiment so that the effect of only temperature of the rate of respiration of yeast will be observed:
- Volume- the volume of both water and yeast solution will be kept constant throughout all the experiments. This will ensure the same proportion of reactants and products react each time.
- Concentration- the concentrations of both glucose and yeast in the yeast solutions must be kept constant as these could effect the rate of respiration as more yeast cells respiring will give the effect of a higher rate and more available glucose will increase the rate.
- Position- the position where the experiments are carried out need to be the same so that if any fluctuations occur they will occur each time.
Diagram:
Method:
Set up the apparatus as shown in the diagram.
Use a syringe to measure 20cm3 of yeast solution and add to one of the boiling tubes.
Simultaneously, measure 20cm3 of distilled water into another syringe
Add the contents of the two syringes into the boiling tubes already assembled making sure not to mix them.
Simultaneously start the timer
Wait 5 minutes and close the three way taps.
Record the initial position of the fluid level in the manometer and then the after closing the taps, record the final position of the fluid.
Using a water bath to maintain temperature, repeat the experiment at 30°C and 40°C.
The distance moved by the fluid can be used to calculate the rate of respiration and the results at room temperature, 30°C and 40°C can be compared.
Conclusion:
The hypothesis for this experiment was that the rate of respiration of yeast would increase with rises in temperature up the last temperature of 40°C. This was found to be the case in the results of the experiment. As the graph ‘A graph to show the change of the rate against temperature’ shows, the rate increases in a fairly constant slope. This is because of the enzymes that catalise the metabolic pathways of respiration. For example at the very first step of respiration in glycolysis, the enzyme phosphofructokinase is used to phosporylate the glucose so that it can be split into to two triose sugars that will eventually produce a pyruvate molecule each. When these pyruvate molecules enter the Kreb Cycle and is converted to acetate, coenzyme A combines with this new compound to assist in the formation of oxaloacetate. Decarboxlases and dehydrogenases are also used in the Kreb Cycle. Then in the last stage of oxidative phosphorylation cytochrome reductase and cytochrome oxidase are used. Thus, as a result of all these enzyme catalysed reactions, the temperature will be a limiting factor and as the rate increases the most between 30°C – 40°C it can be said that the enzymes involved have their optimum temperature within this range.
The prediction was also made that as the temperature increased 10°C the rate would double as a result of the Q10 theory. The experiment showed that this was not exactly the case as the rise of temperature from 20°C to 30°C resulted in an increase in rate by a factor of 1.68 and an increase in temperature from 30°C to 40°C yielded a rate increase by a factor of 1.34. although this is not a consistent factor of two that is being shown, its can be roughly approximated as such. This is significant because the Q10 rule is applicable under ideal condition that were too difficult to obtain in a college laboratory and thus discrepancies are noted.
