1. A 53.8 mg sample of sodium perchlorate contains radioactive chlorie-36 (whose

Question

1. A 53.8 mg sample of sodium perchlorate contains radioactive chlorie-36 (whose atomic mass is 36.0 amu). If 29.6% of the chlorine atoms in the sample are chlorine-36 and the remainder are naturally occuring nonradioactive chlorine atoms, how many disintegrations per second are produced by this sample? The half life of chlorine-36 is 3.0 x 105 yr.

2. Metallic magnesium can be made by the electrolysis of molten MgCl2. a) What mass of Mg is formed by passing a current of 4.55 A through molten MgCl2, for 4.50 days? b) How many minutes are needed to plate out 25.00 g Mg from molten MgCl2 using a 3.50 A of current?

Explanation / Answer

1.
First calculate the number of moles in the sample
Molar mass of NaClO4 = 23 + 36 + 4*16 = 123g
mass of radioactive NaClO4 = 29.6 * 53.8/100 = 15.9248 mg

this corresponds to a number of moles 15.9248 * 10^-3 /123 = 1.295 * 10^-4 m
In atoms of Cl 36, 1.295 * 10^-4 * 6.022 * 10^23 = 7.8*10^19 atoms of Cl-36

To calculate number of disintegrations per seconds use the differential formula dN= -N0*t*lambda
where the lambda radioactive constant is lambda =ln2/half-life

lambda = ln2/(3*10^5 * 365 * 24 * 3600) = 7.32*10^-14 s-1

and result 7.32 * 10^-14 * 7.8*10^19 = 5.71 * 10^6 Bq (Bq = 1desintigration/s)

2.
(a)
equations needed:
* amperes x time = Coulombs
* 96,485 coulombs = 1 Faraday
*1 Faraday = 1 mole of electrons

Rx at anode and cathode:
anode (oxidation): 2 Cl- --> Cl2(g) + 2 e-
cathode (reduction) Mg2+ + 2 e- --> Mg(s)

moles of e-:
4.55 A x 388800 s = 1.77 x10^6 C
(1.77 x10^6 C) x (1/96,485 coulombs) = 18.33 F
18.33F = 18.33 moles e-

moles of Mg and Cl:
(18.33 moles e-) x (1mole Cl/2 moles e-) = 9.17 mole Cl
(18.33 moles e-) x (1mole Mg/2 moles e-) = 9.17 mole Mg

mass of Mg:
9.17 mole Mg x (24.31g Mg/1 mole Mg) = 222.86 g Mg

(b)
Convert Mg to Moles
25.00Mg x (1moleMg/24.31g Mg) = 1.028 mole Mg

half life Rx
cathode (reduction) Mg2+ + 2 e- --> Mg(s)

moles of e to produce moles of Mg
1.028 mole Mg x (2 mole e-/1 moles Mg) = 2.056 moles e-

Convert the moles of electrons into coulombs of charge using Faraday's constant.
2.056 moles e- = 2.056 F
2.056F x (96,485C/1F) = 198,447 C

Calculate the time using the current and the coulombs of charge.
3.50A x t = 198,447 C
t = 566 s
t = 9.45 mins

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