Question

# Part A: Balance each of the following redox reactions occurring in acidic aqueous solution. MnO4−(aq)+Al(s)→Mn2+(aq)+Al3+(aq) Part...

Part A:

Balance each of the following redox reactions occurring in acidic aqueous solution.

MnO4−(aq)+Al(s)→Mn2+(aq)+Al3+(aq)

Part B:

What mass of lead sulfate is formed in a lead-acid storage battery when 1.40 g of Pb undergoes oxidation?

Part C:

A meteor has a Pb−206:U−238 mass ratio of 0.840:1.00.

What is the age of the meteor? (Assume that the meteor did not contain any Pb−206 at the the time of its formation.)

Part A:

Balancing in acidic medium

The reduction equation will be:

MnO4-    --> Mn+2

We will balance oxygen by adding water molecules and then balance hydrogen by adding H+

MnO4- + 8H+      --> Mn+2 + 4H2O

Now balance charge

MnO4-   + 8H+   + 5e --> Mn+2 + 4H2O ...................1

oxidation reaction is

Al --> Al+3 , we need to balance charge only

Al   --> Al+3 + 3e....................2

Now we will add the equation by multiplying with suitable coeffeceients so that charge will be balanced

3MnO4-   + 24H+   + 5Al --> 3Mn+2 + 12H2O + 5Al+3

Part B

The entire redox reaction in lead acid storage battery is
Pb(s) + PbO2(s) + 2H2SO4(aq) --> 2PbSO4(s) + 2H2O(l)

Molecular weight of PbSO4= 303.3 g / mole

Atmoc weight of Pb =207.2 g /mole
As per the balance equation

1 mole of Pb will give 2 moles of PbSO4

so 207.2 grams will give 2X303.3 grams of PbSO4

So 1 gram will give 606.6 / 207.2 grams of PbSO4

so 1.4 gram will give 606.6 X 1.4 / 207.2 grams = 4.102 grams

Part C

As there is no Pb-206 at the start so it is formed only by radioactive decay of uranium

The half-life of uranium decay is 4.47 billion years.,

we know tha t1/2 = 0.693 / K

So K = disintegration constant = 0.155 billion years -1

Now for first order equation

N(t) = N(0) e-Kt

N(t)=Number of uranium atoms at time t

N(0)=Number of uranium atoms initally =N(t)+N(Pb)=sum of uranium and Pb atoms after time t.

N(t)=(N(t)+N(Pb)) e^-kt

or, N(t)/N(t)+N(Pb)=e^-Kt

1+ N(Pb)/N(t)=e^-Kt

N(Pb)/N(t)=e^-Kt-1..........(1)

We have mass ration of Pb / U = 0.840 / 1.0

We know that mole = mass / molecular weight so

Mole ratio = 0.840/1.0 X 238/206 ( atomic weight of Uranium = 238 and Pb = 206)

=0.97/1.00 * NA/NA=N(Pb)/N(t)=0.97/1.00 (NA is avogadro's no)

from eqn (1), 0.97/1.00=e^-kt-1

1.97=e-0.155t

0.678=0.155t

t=4.374 billion years.
This will be the age of meteor