By What Factor Will The Rate Of The Reaction Change If The Ph Decreases From 6.50 To 2.00?

Determining the Activation Energy

It is common knowledge that brianowens.tvical reactions occur more rapidly at higher temperatures. Milk turns sour much more rapidly if stored at room temperature rather than in a refrigerator; butter goes rancid more quickly in the summer than in the winter; and eggs hard-boil more quickly at sea level than in the mountains. For the same reason, cold-blooded animals such as reptiles and insects tend to be more lethargic on cold days.

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The reason for this is not hard to understand. Thermal energy relates direction to motion at the molecular level. As the temperature rises, molecules move faster and collide more vigorously, greatly increasing the likelihood of bond cleavages and rearrangements. Whether it is through the collision theory, transition state theory, or just common sense, brianowens.tvical reactions are typically expected to proceed faster at higher temperatures and slower at lower temperatures.

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Example (PageIndex{1}): Isomerization of Cyclopropane

For the isomerization of cyclopropane to propene,

*

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T, °C

1/T, K–1 × 103

k, s–1

ln k

477 523 577 623
1.33 1.25 1.18 1.11
0.00018 0.0027 0.030 0.26
–8.62 –5.92 –3.51 –1.35

Example (PageIndex{3})

It takes about 3.0 minutes to cook a hard-boiled egg in Los Angeles, but at the higher altitude of Denver, where water boils at 92°C, the cooking time is 4.5 minutes. Use this information to estimate the activation energy for the coagulation of egg albumin protein.

Solution

The ratio of the rate constants at the elevations of Los Angeles and Denver is 4.5/3.0 = 1.5, and the respective temperatures are (373 ;
m{K }) and (365;
m{K}). With the subscripts 2 and 1 referring to Los Angeles and Denver respectively:

<egin{align*} E_a &= dfrac{(8.314)(ln 1.5)}{dfrac{1}{365; m{K}} – dfrac{1}{373 ; m{K}}} \<4pt> &= dfrac{(8.314)(0.405)}{0.00274 ;
m{K^{-1}} – 0.00268 ;
m{K^{-1}}} \ &= dfrac{(3.37;
m{J; mol^{–1} K^{–1}})}{5.87 imes 10^{-5};
m{K^{–1}}}\<4pt> &= 57,400;
m{ J; mol^{–1}} \<4pt> &= 57.4;
m{kJ ;mol^{–1}} end{align*}>

Comment: This low value seems reasonable because thermal denaturation of proteins primarily involves the disruption of relatively weak hydrogen bonds; no covalent bonds are broken (although disulfide bonds can interfere with this interpretation).

The Pre-exponential Factor

Up to this point, the pre-exponential term, (A) in the Arrhenius equation (Equation
ef{1}), has been ignored because it is not directly involved in relating temperature and activation energy, which is the main practical use of the equation.

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What would limit the rate constant if there were no activation energy requirements? The most obvious factor would be the rate at which reactant molecules come into contact. This can be calculated from kinetic molecular theory and is known as the frequency- or collision factor, (Z).

arren_pre_exp.png

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