Not all single displacement reactions that can be written will actually happen in the real world.
For instance, look at the two reactions below
These are (obviously) the same reaction but running in opposite directions.
In the first reaction copper is replacing silver in the compound and in the second, silver is replacing copper in the compound. Logically, only one of those is going to happen. Either nature prefers to have copper in compounds (in which case the first reaction occurs) or nature prefers to have silver in the compound (in which case the second reaction occurs).
Another way to think about this is that if both reactions occur in nature than this mixture would go on reacting forever – the copper kicking out the silver and then the silver kicking out the copper, on and on. We know from experience that reactions don't go forever, so nature clearly favors one over the other.
So, how can we tell which reaction nature prefers? The easy answer is you simply try it in the lab. However, that's not always possible. When we can't do the experiment, we look to a property called activity.
An active element is one that is likely to be found in a compound. In inactive element is one that is likely to be found in pure form. Let's apply that idea to the example above. Copper is known to be more active (more likely to be in a compound) than silver. So the first reaction
makes sense, since the (more active) copper ends up in the compound.
The second reaction:
doesn't make sense. The more active metal (the one more likely to be in a compound) is leaving the compound.
So, we can say that the first reaction (Cu + AgNO3 → ) would occur, because the more active metal goes into the compound, while the second reaction (Ag + Cu(NO3)2 → ) would not occur, because the more active metal is already in the compound.
Here are two more examples:
It is know that iron is more active than gold, so the reaction
would occur, because that would put the more active metal (iron) in the compound.
It is also known that hydrogen is more active than Pt, so the reaction
will NOT occur, because the more active metal is already in the compound.
Now, the real question is how do you (as a student) know which element is more active?
The answer is actually quite simple. There is a list of metals (and hydrogen) from most active to least active called an activity series. You can find one here.
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