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.
To solve this problem using Hess's Law, you can follow these steps:
1. Start by writing the balanced equations for the given reactions:
a) SiO2(s) + 2C(s) → impure Si(s) + 2CO(g) ΔH = 689.9 kJ
b) impure Si(s) + 2Cl2(g) → pure SiCl4(g) ΔH = -657.0 kJ
c) pure SiCl4(g) + 2Mg(s) → 2MgCl(s) + pure Si(s) ΔH = -625.6 kJ
2. Identify the target reaction: SiO2(s) → pure Si(s)
3. Manipulate the given reactions to obtain the target reaction. In this case, you correctly identified that you need the first reaction to get carbon monoxide (CO) and then cancel out the impure silicon (Si). Therefore, you can rewrite the equations as follows:
a) SiO2(s) + 2C(s) → Si(s) + 2CO(g) ΔH = 689.9 kJ
b) Si(s) + 2Cl2(g) → SiCl4(g) ΔH = -657.0 kJ
c) SiCl4(g) + 2Mg(s) → 2MgCl(s) + Si(s) ΔH = -625.6 kJ
4. Multiply the equations as needed to match the stoichiometric coefficients between the target reaction and the given reactions. In this case, we need to multiply equation (a) by 1/2 and equation (c) by 1/2:
a) 1/2 SiO2(s) + C(s) → 1/2 Si(s) + CO(g) ΔH = 344.95 kJ
b) Si(s) + 2Cl2(g) → SiCl4(g) ΔH = -657.0 kJ
c) 1/2 SiCl4(g) + Mg(s) → MgCl(s) + 1/2 Si(s) ΔH = -312.8 kJ
5. Finally, add up the manipulated equations to obtain the target equation:
1/2 SiO2(s) + C(s) + Si(s) + 2Cl2(g) + 1/2 SiCl4(g) + Mg(s) → 1/2 Si(s) + CO(g) + SiCl4(g) + MgCl(s)
ΔH = (344.95 kJ) + (-657.0 kJ) + (-312.8 kJ)
= -624.85 kJ
So, the correct heat of reaction for changing 1 mol of silica (SiO2) into pure silicon (Si) is -624.85 kJ.