**Rate Equation**

In general form, aA+bB→cC,

**rate = k[A]**, where x and y is the^{x}[B]^{y}**order of reaction w.r.t. A and B**, and**x+y is the overall order of reaction**, and k is the rate constant. Note that the rate equation is equation independent.
1)

**Zeroth order reaction**: the order of reaction x or y = 0, which the**rate of reaction is independent of that species**. For example, NH_{3}in Haber process.
2)

**First order reaction**:**rate is proportional to concentration**, Considering rate = k[A], we have half-life of a reactant**t**where k is the rate constant._{0.5}= ln 2/k
3)

**Second order reaction**:**rate is proportional to square of concentration**.
In general case Rate = k[A]

^{n},**ln Rate = ln k + n ln[A]**, we can plot ln(rate)-ln[A] graph, then the y-intersection point is ln k and the slope is the order of reaction.**Energy profile**

It shows the

**enthalpy**(potential energy) and the**reaction coordinate**. The highest point is called at the intermediate where bonds are breaking and forming. When enthalpy drops at the middle it’s called the**transition**state which can be isolated.
The energy difference from initial state and the first

**intermediate**is called the**activation energy**.
The red line shows a

**catalyzed pathway**in which the activation energy is reduced.**Effective collision theory**states that reaction happens only if the two molecules carry enough

**kinetic energy which is larger than the activation energy AND colliding on the right orientation**, e.g. the leaving group.

**Temperature effect on rate of reaction**

**Maxwell-Boltzmann distribution**is a curve of number of

**molecules-kinetic energy**graph and the variation in different temperature is as shown in the picture.

Under same number of molecules,

**1)**

**At higher T, the max. possible freq. decreased.**

**2)**

**The whole curve shifts to the right. i.e. more molecules have higher kinetic energy.**

Comparing curves at different temperatures, at higher temperature the portion of molecules containing enough energy is higher, hence the probability for reaction to occur increased exponentially. By integration result we have the

**Arrhenius equation: k = Ae**, where k is the rate constant, A is a constant independent of the temperature, Ea is the activation energy, R is the^{-Ea/RT}**ideal gas constant**which is numerically 8.31 and T is the absolute temperature. We can conclude that rate of reaction increase exponentially with temperature.
At the same time

**higher k.e. implies higher r.m.s. speed**, then**collision happens more frequently**and further increase the rate of reaction.**Concentration effect on rate of reaction**: High concentration Implies a raise in frequency in collision, but it refers to the rate equation.

**Surface area of solid reactant**: since reaction only occur at the surface of the solid, higher surface area implies more places for reaction to occur, hence faster reaction. It can also be applied to solid catalyst (heterogeneous catalyst).

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