can some one explain to me what is the relationship between enzyme activity and rate of reaction?

The more active an enzyme, the faster it's reaction rate will be. That about sums it up I guess.

 

It also depends on things like cooperative binding and inhibition/activation (as in agonist/antagonist) and also on the type of reaction.

 

Certain enzymes perform really slow reactions (but which would none-the-less take a few thousand years to complete) whereas others can react several times a minute.

 

But the essence is this, activity is proportional to rate.

lets says the optimum pH for XX enzyme is 7. that means the activity and the rate of reaction are higher at pH 7 rather than in pH 6 or 8. right?

Yeah, the optimum conditions for any enzyme (temp, pH, ion concentration) are usually the one's where the enzyme works best without being denatured.

 

There are exceptions, like some enzymes would work better at a higher temperature, but not for a long time, or if they're in biological systems without damaging the host.

 

As a rule of thumb though, you can say that if an enzyme has an optimum pH of 7, it'll work better than if it were at a pH of 6 or 8

alright. thanks man!`