Graphical Method: Order and k from Slope and Intercept

Question

In a study of the rearrangement of ammonium cyanate to urea in aqueous solution at 50 °C

NH₄NCO(aq)(NH₂)₂CO(aq)

the concentration of NH₄NCO was followed as a function of time.

It was found that a graph of 1/[NH₄NCO] versus time in minutes gave a straight line with a slope of 1.67×10^-2 M^-1 min^-1 and a y-intercept of 1.09 M^-1.

Based on this plot, the reaction is _______(zero,first,second) order in NH₄NCO and the rate constant for the reaction is ______M^-1 min^-1.

Answer 1

The fact that a straight line was obtained by graphing [NH₄NCO] v. time tells us that the reaction is 2nd order in NH₄NCO.

The equation for the straight line of this plot is 1/[NH₄NCO] = kt + 1/[NH₄NCO]_o

In this plot, the slope = k and the intercept = 1/[NH₄NCO]_o

rate constant (k) = 1.67x10^-2 M^-1 min^-1