Bukhovtsev-et-al-Problems-in-Elementary-Physics

326 ANSWERS AND SOLUTiONS
to the e. m. f., because in a state of equilibrium the chemical forces that act
in the layer of the electrolyte adjacent to the electrode are equal to the
electrostatic forces.
Since the forces of non..electrostatic origin do not act in the other sections
of the circuit, the work performed by these forces is also equal to the e.m.I.
of the battery when a single positive charge moves along the closed circuit.
(The work of electrostatic forces in a closed circuit is zero.)
481. An energy of W e= 106,000-56,000=50,000 calories e: 2X 10 12 ergs
is liberated per mole of the substances reacting in the cell. Owing to this
energy, the electric current performs the work W = QtR, where B is the e.m.I,
of the cell and Q is the quantity of transferred electricity. Since the copper
and the zinc are bivalent, the charges of their ions are equal in magnitude
to the doubled charge of an electron. One mole of the substance contains
6.02Xl0 23 atoms. Therefore, Q=2X4.8XIO-loX6.02XI023CGSQ.
W
Hence, tG=~e: 3.5X 10- 3 CGS Q = 1.05V.
482. The ratio between the intensities of the currents flowing through the
cells is 11 1 =!::L, since the e.m.f.s of the cells are the same. According to
I '1
Faraday's law, the masses of the dissolved zinc are proportional to the
currents:
483. As it passes into solution in the form of an ion Zn + +, each atom
of the zinc gives off to the external circuit two electrons carrying a charge
of q=2e=-3.2X 10- 19 C. At the same time the copper ions Cur + are depo..
sited on the copper plate as neutral atoms, owing to which the concentration
of the CuS0 4 solution decreases. To maintain the concentration constant, it is
necessary to continually dissolve crystals of CuSO,.5H 20 in an amount that
will compensate for the passing of the ions Cur + and 50;- out of the solution.
According to the initial conditions, a charge of Q =2,880 C passed through
the cell. This corresponds to a transfer into the solution of n =..9-=9X lOtI
q
atoms of zinc, i, e., about 0.98 g of the zinc. Correspondingly, the same
amount of copper atoms (about 0.95 g) will pass out of the solution and 3.73 g
of crystals of blue vitriol will have to be dissolved to restore the concentration
of the CuSO. solution.
484. When the zinc is dissolved, the positive ions Zn+ + pass into solution
and the liberated electrons flow along the wire onto the graphite layer and
neutralize the positive ions of copper in the CuS0 4 solution. Therefore, the
graphite will be covered by a layer of copper.
This phenomenon can be used in galvanoplasty.
485. The change in the e.m.I. of the battery depends on the ratio between
the dimensions of the electrodes and those of the vessel. If the two middle
plates are almost equal in size to the section of the vessel, the e.m.I, of the
battery will change insignificantly. If they are small, the e.m.I, will be
almost halved.
486. The zinc rod forms a short-circuited galvanic cell with each half of
the carbon rod. The resistance of half of the carbon rod, the resistance of the