Question

how do i find the 1st order or 2nd order from this question??

A chemistry graduate student is studying the rate of this reaction

H2CO3 -> H2O +CO2

T	[H2CO3]
0	0.600
1	0.122
2	0.0682
3	0.0472
4	0.0361

1) Write the rate law for this reaction rate = k ()

2) Calculate the value of the rate constant k.

Answer 1

the relation between rate (r) and order (n) -r=-dC/dt= KCⁿ, where C is concentration, n is ordder and K is rate constant

for 1st order, n=1 and hence -dC/dt= KC, when integrated , the equation becomes, lnC= lnCO-Kt, CO= initial concentration of reactant. So a plot of lnC vs time gives straight line if the reaction is 1st order with the slope being-K.

for second order -dC/dt= KC², when integrated,1/C= 1/CO+ Kt, so for second order reaction a plot of 1/C vs t gives straight line

so a plot of lnC vs t   is drawn to verify whether it is a straight line.

the data is not a good fir for the 1st order as seen from R2 value.

hence 1/C vs t plot is drawn to check whether the graph is straight line or not.

the plot is straight line with R2 value of 1 and is the best fit.

From the graph, the reaction is second order and slope is rate constant, K= 6.505/concentrion units. time units

rate law is -r= 6.505[H2CO3]²