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Describe the graphical representation of first order reaction. |
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Answer» Solution :REACTION whose rate depends on the reactant concentration raised to the first power is called a first order reaction. Let us CONSIDER the following `Cl_(2)` first order reaction, `A rarr` product Rate law can be expressed as Rate `= k[A]^(1)` Where, k is the first order rate CONSTANT. `(-d[A])/(dt)=k[A]^(1)` `rArr (-d[A])/([A])="k dt"`....(1) Integrate the above equation between the limits of time t = 0 and time equal to t, while the concentration varies from the initial concentration `[A_(0)]`to [A] at the later time. `int_([A_(0)])^([A])(-d[A])/([A])=k int_(0)^(t)dt` `(-In[A])_([A_(0)])^([A])=k(t)_(0)^(t)` `-In[A]-(In[A_(0)])=k(t-0)` `-In[A] - In[A_(0)]=kt` `In(([A_(0)])/([A]))=kt ""`....(2) This equation is innatural logarithm. To convert it into usual logarithm with base 10, we have to multiply the term by 2.303.  A plot og ln[A] Vs t for a first order reaction, `A rarr` product with initial concentration of `[A] = 1.00 M` and `k = 2.5xx10^(-2)"min"^(-1)` `2.303 log(([A_(0)])/([A]))=kt` `k=(2.303)/(t)log(([A_(0)])/([A]))""`.....(3) Equation (2) can be written in the form `y=mx + c` as below `In [A_(0)]- In [A] = kt` `In[A] = In[A_(0)]-kt` `rArr y = c + mx` If we follow the reaction by measuring the concentration of the reactants at regular time interval 't', a plot of In [A] againt 't' yields a straight line with a negative SLOPE. From this, the rate constant is calculated. |
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