Why Is the Sum of I2 to I5 Used in This Ionization Energy Calculation?

[Hooke's Law]

Homework Statement

I1, = 786 kJ molG1 I5 = 16,091 kJ molG1
I2 = 1577 kJ molG1 I6 = 19,784 kJ molG1
I3 = 3232 kJ molG1 I7 = 23,766 kJ molG1
I4 = 4355 kJ molG1 I8 = 29,251 kJ molG1

Determine the energy required in kJ molG1 for the following process:
M(g)^+ ------> M^5+(g) + 4 e

The Attempt at a Solution

I saw the solution sheet and it says "E = 25,255 kJ/mol (Sum of I2, I3, I4 and I5) Use Hess’s Law"

But why is it I2 to I5 and I thought it should be (products - reactants)
which I thought is I6 - I2. Could someone explain to me?

Thanks

 

[Borek]

Write reaction equation for each Ix.

 

[Hooke's Law]

I1 =M(g) ---> M^+(g) +e
I2= M+(g) ----> M2+ + e
I3 =M2+ ----> M3+ + e
I4 = M3+ ----> M4+ +e
I5 = M4+ ----> M5+ + e
I6 =M5+ ----M6 + +e

What's next?

 

[Hooke's Law]

Did I do them right?

 

[Borek]

OK, now, which reactions have to be combined?

 

[Hooke's Law]

I still don't understand. What I'm thinking is still I6 - I1...

 

[Borek]

I1 is about starting with Mg(0) - do you have Mg(0) in the process?

 

[Hooke's Law]

No, I1 won't be in the process.

 

[Borek]

What if I tell you that I6 is NOT Mg(0) -> Mg⁶⁺?

 

[Hooke's Law]

Oh in my other previous post it should I6-I2. For I6 isn't it I6 =M5+ ----M6 + +e?

 

[Borek]

Yes, I6 is Mg⁵⁺ -> Mg⁶⁺.

What reactions are needed to go from Mg(0) to Mg²⁺? Is I1 enough, or do you need I1 AND I2?

 

[Hooke's Law]

I'm thinking I1 and I2 is needed.

 

[Borek]

Yes, you need both. Now, which ones do you need to go from Mg⁺ to Mg⁵⁺?