Kevin M. answered 08/28/15
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The metal activity series below is ordered in terms of each metal's reactivity - the higher it is on the list, the more reactive it is (this activity series is just for metals; there's a similar one for nonmetals provided further down this answer). What this means is that a metal can "replace" any metal that is lower than itself in the series. What does "replace" mean? Metals strongly prefer to be in their ionic - i.e. oxidized - state (i.e. with a positive charge), so they're desperately looking for a way to give away one or more electrons to make this happen. This means another element has to take the electron.
For example in the following equation, on the reactant side copper is in its pure elemental (neutral) form, and silver is in the preferred ionic form (+1 charge). On the products side, copper is in its preferred ionic form (+2 charge) while silver (against its preference) went back to being neutral:
Cu + 2AgNO3 --> Cu(NO3)2 + Ag
(Remember, in AgNO3 silver is Ag+, which balances the NO3- ion, and in Cu(NO3)2 copper is Cu2+ to balance the two NO3- ions).
This reaction is only allowed to happen if copper is more reactive than silver - copper has to "bully" the silver ions into taking its electrons so it can transition to its preferred ionic form (+2). The reaction cannot go in reverse - silver isn't enough of a "bully" to make the copper ion take the electrons back ..... silver is lower than copper in the activity series.
METAL REACTIVITY SERIES:
K
Na
Li
Ba
Sr
Ca
Mg
Al
Mn
Zn
Cr
Fe
Cd
Co
Ni
Sn
Pb
Li
Ba
Sr
Ca
Mg
Al
Mn
Zn
Cr
Fe
Cd
Co
Ni
Sn
Pb
H2
Sb
Bi
Cu
Hg
Ag
Au
Pt
Sb
Bi
Cu
Hg
Ag
Au
Pt
For nonmetals the activity series works the same way - a nonmetal can replace any other nonmetal lower than itself in the series. Like metals, nonmetals prefer to be in their ionic state - but this is the reduced form since nonmetals form negative ions. A nonmetal reactivity series is below:
F2
Cl2
Br2
I2
In the examples you proposed, ask yourself, 1) "Who is the free, single element doing the replacing?" and 2) "Is this element capable of replacing the element currently bonded within a compound?" The answer to this second question is yes if the free/single element is higher than the element it's replacing. Bear in mind, metals only replace other metals, and nonmetals only replace other nonmetals
1) Ni(s) + H2O(l) →
2) Br2(l) + KI(aq) →
3) Au(s) + HCl(aq) →
4) Cd(s) + HCl(aq) →
5) Mg(s) + Co(NO3)2(aq)
2) Br2(l) + KI(aq) →
3) Au(s) + HCl(aq) →
4) Cd(s) + HCl(aq) →
5) Mg(s) + Co(NO3)2(aq)
1) Ni (a metal) is trying to replace H2 (not a true metal, but a metallic element that forms a +1 ion). Looking at the metal reactivity series, Ni is higher than H2 so the reaction will happen: Ni(s) + H2O(l) → NiO + H2
2) Br2 (a nonmetal) is trying to replace the I- ion (a nonmetal) in KI. Looking at the nonmetal reactivity series, Br2 is higher than I2 so the reaction will happen: Br2(l) + 2KI(aq) → I2 + 2KBr
3) Au (a metal) is trying to replace H2. Au is lower than H2 in the reactivity series, so the reaction cannot happen.
4) Cd (a metal) is trying to replace H2. Cd is higher than H2 in the reactivty series, so the reaction will happen: Cd(s) + 2HCl(aq) → CdCl2 + H2
5) Mg (a metal) is trying to replace Co (also a metal). Mg is higher in the reactivity series, so the reaction will happen: Mg(s) + Co(NO3)2(aq) --> Mg(NO3)2 + Co