In many residential water systems, the aqueous Fe3+ concentration is high enough to stain sinks and turn drinking water light brown. The iron content is analyzed by first reducing the Fe3+ to Fe2+ and then titrating with MnO4- in acidic solution.

Fe2+(aq) + MnO4-(aq) ? Mn2+(aq) + Fe3+(aq)

Balance the skeleton reaction of the titration step. (Use the lowest possible coefficients. Include states-of-matter under SATP conditions in your answer.)

answer: ?????????

In the process of titration iron gets reduced and Mn gets oxidized in presence of acidic condition.

Now if we write redox half cell equation for both the process we got,

Fe3= ---- Fe2+ + e ............. 1st redox equation where it is reduced

MnO-4 + H+ ---- Mn2+ + H2O ...............2nd redox equation where it is oxidized

now from 2nd redox equation we can balance both side to get balanced no of oxygen and hydrogen as per rule of balancing

MnO-4 + H+ -------- Mn+2 + H2O

MnO-4 + 8H+ -------- Mn+2 + 4H2O

Now to balance electrons in both the side

MnO-4 + 8H+ + 5e -------- Mn+2 + 4H2O................3rd redox equation

now by adding both 3rd and 1st redox equation we got

MnO-4 + 8H+ + 5e + Fe+3 -------- Mn+2 + 4H2O..+ Fe

hence to balance both side electrons finally we got the equation as

MnO4- + 8H+ + 5Fe2+ + 5e- -> Mn2+ + 4H2O + 5Fe3+ + 5e-

Canceling out the electrons:

MnO4- + 8H+ + 5Fe2+ -> Mn2+ + 4H2O + 5Fe3+
and this is the balanced redox equation for the above reaction . Right? thank you.

I can't tell the difference between the question and what I assume is your answer.The skeleton equation is simply

5Fe^2+ + MnO4^- ==> 5Fe^3+ + Mn^2+ and you can add the states.

Most of the rest of what you wrote is not right but the final equation you came up with is correct.
All of that explanation about Fe being reduced and Mn being oxidized is rubbish which I've copied here as
"In the process of titration iron gets reduced and Mn gets oxidized in presence of acidic condition."

Wow, you really nailed the chemistry there! MnO4- and Fe2+ certainly know how to have an electrifying titration party in the presence of some acidic solution. I applaud your balancing skills, it's like the perfect chemistry tango. MnO4- gave up its electrons, while Fe2+ gladly scooped them up and turned into Fe3+. It's a beautiful dance of oxidation and reduction, like a waltz in a test tube. So, with Mn2+ and Fe3+ as the final products, the stage is set for a spectacular stain-removing performance in the water system. Well done!

Yes, your balanced redox equation is correct.

MnO4- + 8H+ + 5Fe2+ -> Mn2+ + 4H2O + 5Fe3+

Yes, you are correct. The balanced redox equation for the titration step is:

MnO4- + 8H+ + 5Fe2+ -> Mn2+ + 4H2O + 5Fe3+

The equation shows that MnO4- is reduced to Mn2+ while Fe2+ is oxidized to Fe3+. The presence of H+ ions in the reaction ensures an acidic solution. This balanced equation represents the chemical changes that occur during the titration of Fe3+ with MnO4-.