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1. Integrate	the	differential	first‐order	rate	law	dcA/dt	=	–1kcA	(1k	=	1	s–1)	using	
Euler’s	approximation	(4	steps,	cA(0)	=	1	M,	∆t	=	0.1	s)	starting	at	t	=	0	and	
compare	with	the	exact	result.	
	
2.	 a)	Given	the	following	reaction	mechanism,	write	the	system	of	coupled	
differential	equations	for	the	reactions	of	compounds	A1	to	A3.	
	
	
	
	
b)	The	rate	constants	are	k2	=	1	s–1,	k3	=	1000	s–1,	and	k–3	=	100	s–1.	Which	
approximations	are	applicable	to	simplify	the	integration	of	these	equations?	
c)	Sketch	the	expected	concentration	profiles	qualitatively	for	case	b)	in	the	
diagram	below,	given	that	the	initial	conditions	are	c1(t=0)	=	1	M,	c2(0)	=	
c3(0)	=	0	M	(indicate	the	time	scale).			
	
		 	
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3.	 Interpret	 the	 three	 legs	 of	 the	 pH–Rate	 profile	 for	 the	 enolization	 of	 2,4‐
cyclohexadienone	to	phenol.	a)	left:	slope	–1,	b)	middle:	slope	0,	c)	right:	slope	
+1].	Give	the	observed	rate	law,	c(t)	=	...,	holding	in	the	linear	region	of	each	leg	
and	 propose	 a	 reasonable	 mechanism	 for	 each.	 Hints	 a)	 The	 protonation	 of	
carbonyl	 oxygen	 is	 not	 rate‐determining.	 b)	 The	 reaction	 is	 not	 an	
intramolecular	 1,3‐H	 shift	 (the	 reaction	 is	 much	 slower	 in	 aprotic	 solvents).	
Hint:	The	enolization	reaction	is	(practically)	irreversible.