rate of a chemical reaction

[chemilover]

hello there to all respectable science lovers

 

i would like to ask about the rate of a chemical reaction

 

my question is:

 

why rate expression for the reactants is taken with negative sign?

e.g. A+B ----> C+D the rate expression for the reactants is

dx/dt=-[A]

 

 

i need some clarification as i teach chemistry

thanks

sincerely

chemilover

[woelen]

It depends on what your x is. If x = [A] or x = , then you indeed have a negative sign, but if x = [C] or x = [D], then you have the positive sign.

 

This can easily be explained. The rate of reaction in this case is k*[A]* for some positive constant k. But while this reaction is running, compounds A and B are consumed, while at the same time compounds C and D are produced.

 

So, the concentration of [A] and decreases, and the rate at which this happens is k*[A]*. so, d[A]/dt = -k*[A]*, and the same is true for d/dt.

 

The concentration of [C] and [D] increases, and hence a positive sign is used for these: d[C]/dt = k*[A]*.

 

If you were going to solve these differential equations, then you'll see that the concentration of [A] and decreases, but the reaction goes slower and slower. At the same time [C] and [D] increase, but the rate at which this happens also is slower and slower.

[chemilover]

hey thanks woelen

what i predict from your answer is that as the concentration of the reactants continuously decreases the expression comes to be negative also,we introduce negative sign so as to make the expression positive

[woelen]

what i predict from your answer is that as the concentration of the reactants continuously decreases the expression comes to be negative also,we introduce negative sign so as to make the expression positive

No, none of the expressions will become negative. The minus-sign is not there to prevent the expression from becoming negative, it reflects the consumption of A and B.

 

The concentration of either A or B will go to 0 asymptotically (the one with the lowest initial concentration) at an exponential rate. Have a look at the equation dx/dt = -kx. It will go to 0 as x(t) = x(0)*exp(-kt), where x(0) is the initial value of x and x(t) is the value of x at time t.

Of course, the model of the reaction is more complicated, but qualitatively, the model has similar behavior for the compound with lowest initial concentration.

[John Cuthber]

The reactants get turned into products so, at any given time the rate of change of ammount of reactant with time is negative.

Imagine we start with a gram of reactant and that after 5 minutes there is half a gram left. The change in amount of reactant is minus half a gram and the change in time is 5 minutes so the rate of change is -0.5/5 ie -0.1g/min

Since we prefer our constants to be positive we chose to use the expression

dx/dt=-k[A] (with a minus sign in it.)

It's a matter of convention; we could use rate negative constants but they would look odd.