Corks Lab Example

In lab we often do the cork experiment where we find the order of reaction for the blue colored corks when they are tossed back and forth for 20 seconds. Use the data given below to calculate the order of the blue corks with its uncertainty.

Expt.	#W Before	#B Before	#Blanks Before	#B After	Average #B	Time	Init. Rate
#1	30	30	40	7,13,12	10.7	20 sec	0.533
#2	30	50	20	20,19,21	20	20 sec	1.000
#3	30	70	0	25,31,34	30	20 sec	1.500

Answer

Expt.	[W]	[B]	Rate
#1	0.300	0.300	0.533
#2	0.300	0.500	1.000
#3	0.300	0.700	1.500

Remember:

rate = k[W]^x[B]^y

When dividing one rate by another the k will always cancel and, if one of the concentrations remains constant, it will also cancel. In this case the k and [W]^x will always cancel.

rate₂/rate₁ = 1.0/0.533 = (0.5)^y/(0.3)^y = (0.5/0.3)^y

⇒ 1.875 =(1.67)^y ⇒ ln(1.875)=y[ln(1.67)] and y = (ln 1.875)/(ln 1.67) = 1.226

rate₂/rate₃ = 1.0/1.5 = (0.5)^y/(0.7)^y = (0.5/0.7)^y

⇒ 0.667 =(0.714)^y ⇒ ln(0.667)=y[ln(0.714)] and y = (ln 0.667)/(ln 0.714) = 1.204

rate₁/rate₃ = 0.533/1.5 = (0.3)^y/(0.7)^y = (0.3/0.7 )^y

⇒ 0.355 =(0.429)^y ⇒ ln(0.355)=y[ln(0.429)] and y = (ln 0.355)/(ln 0.429) = 1.222

Average y = 1.2174, range = 0.022, ± = range/2 = 0.011

⇒ Result = average ± range/2 = 1.2174 ± 0.011

Or, when properly rounded y = 1.22 ± 0.02