New AP Chem Question for Dr. Bob

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This is a Hess' Law problem. I think I got it but I'm hoping you could check it for me:

Calculate the heat of reaction for changing 1 mol of silica, SiO2, that has been extracted from sand into the pure silicon that is needed to make computer chips. Use the following data:

SiO2(s)+2C(s)->impure Si(s)+2CO(g)
.....delta H = 689.9 kJ
impure Si(s)+2Cl2(g)->pure SiCl4(g)
.....delta H = -657.0 kJ
pure SiCl4(g)+2Mg(s)->2MgCl(s)+pure Si(s)
.....delta H = -625.6 kJ

I started with trying to get
SiO2->Si+O2
but I realized there was no plain oxygen anywhere. I concluded that I needed the first reaction with carbon to carbon monoxide and made my equation
SiO2+2C->Si+2CO
I didn't have to change around any equations and just added the delta H's to get -592.7 kJ.

I think that's right. I obtained the same answer and I added the equations as they were written.

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