Half life of second order reaction full#

The initial concentration, half that would be right here. To go from eight to four? Alright we can find that on our graph. Alright so we're left with four molecules so I'll draw those in there and how long did it take Alright, so if we waitįor the concentration to decrease to half its initial, what are we left with? We were left with four molecules. With eight particles that are eight molecules so here we have one, two, three, four, five, six, seven, eight. And let's just do a made-up reaction here. So here is our initial concentration of A. On the graph would be the initial concentration of A. So when time is equal to zero, alright, this point right here Of concentration versus time for a second order reaction so we can understand this conceptĪ little bit better. For a first order reaction we saw that the half-life was constant but here the half-life isn't constant because the half-life depends on the initial concentration of A. Notice this is very different for the half-life for a first order reaction. And so here's our equation for the half-life for a second order reaction. So we get the half-life is equal to one over k times the initial concentration of A. The initial concentration of A and that's equal to the rate constant k times the half-life. Initial concentration of A minus one over the initialĬoncentration of A? That would just be one over Initial concentration of A is equal to k t1/2. So one the left side this would just be two over the initial concentration of A minus one over the Initial concentration of A divided by two minus one over the initial concentration of A is equal to the rate constant k times the half-life.

So it's half of our initial concentration. So our initialĬoncentration would be this. T 1/2 in for the time what's the concentration of A? Well using the definition for half-life, the concentration of A should be half of the initial concentration. Time is equal to t 1/2 so we're going to plug So if we're talking about the half-life so that would be when

One over the concentration of A minus one over the initial concentration of A is equal to the rateĬonstant k times the time. Integrated rate equation for a second order reaction. We've also already talked about the integrated rate law or the Time that it takes for the concentration ofĪ reactant to decrease to half of its initial concentration.

Remember half-life is symbolized by t 1/2. Khan Academy: Rate law and reaction order.Second-order rate law (differential form).is the concentration of substance A at a certain time during the reaction in units of (mol/L).k is the rate law constant in units of (L/mol* sec).t is the time or the duration of the reaction in units of (sec).

0 is the initial concentration of A in units of (mol/L).

is the end concentration in moles per liter (mol/L).

The Second-order rate law (integral form) equation is Second-order rate law (integral form) Formula Since the concentrations are the same, the substances can be treated as one and the integration becomes just like in case 1. The reactants are of two different substance (A and B) but their concentrations are the same. When both of the reactants are different and have different concentrations the differential equation is integrated differently giving the equationĬase 3. The reactants are of two different substances (A and B) and their concentrations are different The integrated rate equation is as show above.Ĭase 2. Since both of the reactants are the same, the concentration is the same for both of the reactants. Both of the reactants are of the same substance A Unlike the first-order rate law, the second-order depends on two reactants and thus there are three different cases:Ĭase 1.

Half life of second order reaction full#

The integral form of the equation was obtained from the differential form and the full integration can be found here. The second-order rate law equation, specifically the integral form looks at the concentration of the reactants at a certain point in time. However this can be automatically converted to compatible units via the pull-down menu. 0 Initial Concentration of SubstanceĬoncentration t: The calculator returns the concentration in moles per liter.INSTRUCTIONS: Choose units and enter the following: The Second -order Rate Law (Integral Form) calculator computes the second order rate (concentration) based on the concentration of substance, rate the constant and duration of time.