# On passing 10 amperes of current for 50 minutes, 2.4 gm of a metal is deposited . The equivalent weight of the metal is

1
by shireenprince

2015-04-22T18:27:16+05:30

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The formula  for equivalent weight :  E
mass of metal deposited on electrode:  m = 2.4 gms
current strength i = 10 A
time duration  t = 50 min = 3, 000 sec.
charge = i t = 30, 000 Coulombs

96, 500 m =  E * i * t

E =  96, 500 * m / ( i t )  = 96, 500 * 2.4 / 30, 000 = 7.72

The atomic weight if the metal is univalent :  7.72
The atomic weight if the metal is divalent : valency 2:    15.42

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alternate way to do the above exercise:

the charge :  10 A *  50 * 60 sec = 30, 000 Coulombs.
equivalent to   30, 000 /1.602 * 10⁻¹⁹  = 1.8726 * 10²³ protons.  So this many ions with single charge on them have travelled to the electrode.

If the metal is a single charge carrying one (single valency) then:
weight of a metal ion :  2.4 gm / 1.8726 * 10²³ = 1.253 * 10⁻²³  gm
weight of one mole of metal ions :  1.253 * 10⁻²³ * 6.023 * 10²³  = 7.72

if the metal has valency 2 , then its atomic weight will be : 15.438