We're gonna calculate the lattice energy here for
calcium hydride, and essentially what that means is
calculating deltaH for the reaction of calcium ion in the gas phase
and then hydrogen ion in the gas phase. Going to make calcium
hydride solid. And we're given these various steps
that we can combine to make this overall reaction
and when we do that, can we conbine their deltaH's
This is the idea of this Borne-Hopper cycle.
So what we're going to do is figure out how we combine
these reactions. We're starting with calcium ion
Let's work with that first. So this is how we can imagine
this processes taking place. Start with calcium 2 plus
and these are gas phase, this one too, so
calcium 2 plus in the gas phase
have an electron, calcium plus, well deltaH for that reaction
is the negative of this deltaH, since it's reverse
of this reaction. So this is -1145 kJ
for this one mole that we're carrying out the reaction
And then the calcium plus, and just to be clear
remember these are gas phase. We add another electron
to that, we can make calcium in the gas phase
that is the reverse of this reaction, so
that means that the negative of that reaction is
deltaH for the second reaction. And then we're going to
take calcium in the gas phase and condense to make
the solid, and then we're doing this because we can see
this reaction, which gives us the calcium hydride
solid requires calcium solid, so that's the reverse of this
reaction here, and so therefore deltaH is the negative
of deltaH for that reaction. Next we're going to
take H minus in the gas phase since that's reactant
and I'm gonna get H plus an electron
So as reverse of this reaction, so this is plus 72.8 kJ
and then because we have two hydrogen ions, in this
original reaction, we're gonna multiply this by two
which means we need to multiply deltaH by two
And then we're gonna take two hydrogens, and rememeber this is gas phase
and we're gonna make H2 in the gas phase
and that's the reverse of this reaction
So -4335.9 kJ, note this reaction here is for two hydrogens
The last step is to take calcium solid, that we formed in this step
and react with hydrogen which we formed in this step
to make calcium hydride solid, our desired product for
this reaction, and so deltaH is -186.2 kJ
So the idea is then, if we've done this correctly we add
up these reactions and we should get our desired reaction
And if that's true we can add up these deltaH's
so get our desired deltaH. What we want to do then is
go through and cancel out whats on both sides of the
equation. In other words we have calcium plus on both
sides of the equation, we add them together and these will cancel
Likewise calcium in the gas phase, calcium solid
H2, H2, two H's because of the two here and
two electrons here, and then because this equation
is multiplied by two, so the electrons also cancel, so if
we've done this correctly, what we have left is calcium
two plus in the gas phase, plus two H's in the gas phase
makes calcium hydride solid
and if we add these together, we get -2389.5 kJ