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It is customary that the unique reaction rate is positive, because you're describing the rate at which the reaction proceeds as time progresses. Thus, you negate the reactant rate (d[R]/dt) (and if needed, divide by the stoichiometric coefficient of R) to get the positive unique reaction rate.
We usually want the rate to be a positive number because it might seem unusual for a rate to be a negative number. Thus, when we calculate the rate of a reactant, we usually add the negative sign in front of the change of concentration over change in time. This is because the change in concentration is probably negative for reactants, so by adding another negative in front of a negative, we would make this rate positive.
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