Can someone please help me with this problem?

An iron nail placed in a beaker with a solution of silver nitrate will cause pure silver to collect on the bottom of the beaker. Write a balanced equation for the reaction that occurs.

This is what I have so far:
Fe + AgNO3 ---> Ag

Fe goes to Fe++ .
Ag+ goes to Ago

Don't forget that the electrons exchanged must balance AS WELL AS the atoms and the charges.

Sorry, but what do you mean by this?:

Fe goes to Fe++ .
Ag+ goes to Ago

The iron ends up as Fe^++ and the silver ends up as silver metal,(Ag^o).
Fe + 2AgNO3 ==> Fe(NO3)2 + 2Ag.

Thanks. Do you think you can explain why, though?

Have you studied about the activity series of metals (sometimes called the electromotive force series)? The activity table of metals is a list in which the metals at the top of the list will REPLACE the ion of any metal below it in the table. Fe is about midway in the table; Ag is near the bottom. Therefore, Fe will go into solution and Ag ion will come out. That is what happened in your experiment. The iron dissolved and the silver plated out onto the iron nail (or rod or whatever you used). The nitrate ion is a spectator ion; i.e., it never entered into the reaction. When two silver atoms plated out, it left two nitrate ions unattended and they become cozy with the iron atom that has just gone into solution. The first equations I wrote were a prelude to what I hope you would write as the two half reactions that take place. They are oxidation-reduction reactions. They are
Fe==> Fe^+2 + 2e
2Ag^+ + 2e ==> 2Ag.
----------------------
Then add the two equations to get the overall net ionic equation.
Fe + 2Ag^+ + 2e ==> Fe^+2 + 2e + 2Ag
And the two electrons cancel with each other since they appear on both sides of the equation. I hope that helps. If I got too fancy, let me know what grade you are in and I can tailor the explanation a bit.

I'm in 10th grade. We just started talking about that, so it makes sense for the most part. We didn't actually do the experiment. Thank you for all of the help!

What element will cause the iron in the solution to come out if the iron remains?

You're welcome! I'm glad I could help. If you have any more questions or need further clarification, feel free to ask. Good luck with your studies!

You're welcome! I'm glad I could help. It's great to hear that you're already learning about oxidation-reduction reactions and the activity series of metals in 10th grade.

In this case, the reaction between iron (Fe) and silver nitrate (AgNO3) is an example of a single displacement reaction. The iron atoms in the nail react with the silver ions in the silver nitrate solution, causing the iron to dissolve as Fe^+2 ions and silver to be deposited as Ag metal.

The balanced equation for the reaction is:
Fe + 2AgNO3 → Fe(NO3)2 + 2Ag

In this equation, the iron (Fe) displaces the silver (Ag) from the silver nitrate (AgNO3) to form iron(II) nitrate (Fe(NO3)2) and silver metal (Ag).

To balance the equation, you need to ensure that the number of atoms of each element is the same on both sides of the equation. In this case, there is one iron atom and two silver atoms on each side, as well as two nitrate ions (NO3^-). Therefore, the equation is balanced.

If you have any more questions or need further clarification, feel free to ask!