What determines whether one metal will replace another metal from a compound in a single-replacement reaction?

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I found this for you. I hope will work for you.
Displacement occurs when they is an obvious difference in reactivity for both the metals. e.g: If you got Rubidium and Sodium, obviously rubidium got the better reactivity, hence it will displace any sodium compound in any reaction unless you got something more reactive than rubidium.

In a single-replacement reaction, one metal replaces another metal from a compound based on the reactivity of the metals. The reactivity of metals is determined by their position in the reactivity series. The reactivity series is a ranking of metals in order of their reactivity, with the most reactive metals at the top and the least reactive metals at the bottom.

To determine whether one metal will replace another metal from a compound in a single-replacement reaction, you can compare their positions in the reactivity series. If the metal attempting to replace another metal is higher in the reactivity series, it will be able to replace the metal in the compound. On the other hand, if the metal attempting to replace another metal is lower in the reactivity series, it will not be able to replace the metal in the compound.

For example, if you have a compound like copper sulfate (CuSO4) and you want to know if zinc (Zn) can replace copper (Cu) in this compound, you can consult the reactivity series. Zinc is higher in the reactivity series than copper, so in this case, zinc will be able to replace copper from the compound, resulting in zinc sulfate (ZnSO4) and copper.

It is important to note that the reactivity series is a general trend and there may be exceptions in specific situations due to other factors such as concentration and temperature.