Cliffs AP Chemistry, 3rd Edition

2. Radon-222 can be produced from the α-decay of radium-226.
   (a) Write the nuclear reaction.
   (b) Calculate ∆E(in kJ) when 7.00 g of^22688 Radecays.

24 He=4 0015./g mole

(^22286) Rn=221 9703./g mole
(^22688) Ra=225 9771./g mole
(c) Calculate the mass defect of^22688 Ra.
1 mole protons = 1.00728 g
1 mole neutrons = 1.00867 g
atomic mass^22688 Ra=225 9771./g mole
(d) Calculate the binding energy (in kJ/mole) of^22688 Ra.
(e)^22688 Rahas a half-life of 1.62 × 103 yr. Calculate the first-order rate constant.
(f) Calculate the fraction of^22688 Rathat will remain after 100.0 yr.
Answer

2. Given:^22286 Rnproduced by α-decay of^22688 Ra.
   (a) Restatement: Nuclear reaction.

(^22688) Ra" (^22286) Rn+ (^42) He
(b) Given: 7.00 g of 88226 Radecays.
Restatement: Calculate ∆E(in kJ).
∆E= ∆mc^2
=900 10. ##^10 kJg ∆m
∆m= mass products −mass reactants
= 4.0015 g + 221.9703 g −225.9771 g
= −0.0053 g
.
.

..
E.
g

g

∆ 1

700

225 9771

1

1

0 0053 900 10

15 10

gRa

Ra

mole Ra

mole Ra g

(^88) kJ kJ
226
88
226
88
226
88
226
(^107)
= #### #

• =-

(c) Restatement: Mass defect of^22688 Ra.

..

..

.

moles protons g g

moles neutrons g g

g

88 88 1 00728 88 6406

138 138 1 00867 139 196

227 837

#

#

==

==+

mass defect = 227.837 g −225.9771 g = 1.860 g

Part II: Specific Topics