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The rate constant is deemed a constant for a specific reaction at a specific, constant temperature. This differs from reaction rate because the rate of reaction is the speed in which a reaction is occurring. A good way to think about it is that concentration increasing or decreasing may change the reaction rate while because the rate constant is simiply a scalar of reactant concentrations, it can't change in response.
The reaction rate how fast a chemical reaction occurs when going from R-->P. A reaction rate constant gives the comparative amount of the reaction rates of reactants and products. Meaning that the rate of reaction is influenced the types of reaction, the concentration, pressure, and the temperature when the reactions occurs. The reaction rate constant is influenced only by the temperature or a catalyst-->the reaction rate constant will not change if the only thing changed is the concentration of R
Also, the rate constant (K) is considered the slope of the graph showing rate of reaction. For first order reactions, the y axis is ln(molar concentration) versus the x axis of time, and the resulting line plotted has a slope of -K, and for second order reactions the y axis is 1/(molar concentration) versus time, and the resulting slop is K.
Rate constant is just a constant of proportionality relating how the concentrations of the participants of the reaction relate to the rate of reaction. The rate itself just shows how fast the concentration of one of the participants changes, in units of concentration/pressure per unit time. The rate constant is specific to the reaction and the temperature, so if the rate of reaction increases due to the concentrations of reactants or products increasing (and vice versa), the rate constant will not change.
A rate constant is simply a proportionality constant included in the rate law. A reaction rate is the actual rate of a reaction, so it tells us how long it takes for reactant to be used up and product to be formed. While a reaction rate always includes units of time, the units of a rate constant vary (units depend on order of reaction).
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