How to Simplify Zinc-AgNO3 Redox Reaction Calculations?

[Mandelbroth]

Homework Statement

From 9th edition of Raymond Chang's Chemistry (Problem 4.108):
"When 2.50 g of zinc strip were placed in a AgNO₃ solution, silver metal formed on the surface of the strip. After some time had passed, the strip was removed from the solution, dried, and weighed. If the mass of the strip was 3.37 g, calculate the mass of Ag and Zn metals present."

Homework Equations

$Zn + 2AgNO_3 \rightarrow 2Ag + Zn(NO_3)_2$

The Attempt at a Solution

I'm, honestly, more of a math person. Because it was indicated that the reaction was not exactly like the chemical equation above (id est, not all the zinc was made into zinc nitrate), I decided I'd make a mathematical equation to represent it.

Thus, I came to $M_{Ag}\left(2(m_{Ag} - m_{Zn})\right) + M_{Zn}m_{Zn} = 3.37$, where M is the molar mass of the respective element, m_Ag is the theoretical number of moles of silver if all the zinc was made into zinc nitrate, and m_Zn is the actual number of moles of zinc remaining on the strip. Solving for m_Zn, we get 0.0324456474... mol Zn. Thus, the mass of Zn is around 2.12 g, and therefore the mass of Ag is around 1.25 g. This is the correct answer given in the back of the book.

The question is: "Is there an easier way?"

 

[SteamKing]

There's no rule that says you can't mix math and chemistry.

You have solved the problem in a simple and efficient way.