[JuniorAAAHAHS]

I don't understand how in this image: https://imgur.com/a/ljr00lX , The square on [H] was removed. If anything shouldn't be multiplied with 0.3?
Question:
Calculate pH of solution containing 0.1M HS and 0.3M HCl. Ka = 1.2*10^-20

[Borek]

As far as I can tell not only square was lost, but also concentration of H⁺ should be 0.3+2Cα, not 0.3+Cα. Looks like a careless mistake to me.

And no, it shouldn't be multiplied just by 0.3, it should be squared. Although assuming concentration of H⁺ is just 0.3 is a very good approximation in this case, as the dissociation of H₂S produces H⁺ in the 10^-7 range.

[JuniorAAAHAHS]

I don't understand why it should be added though?

[Borek]

In Ka you need to account for a total concentration of an ion, which is a sum of concentrations coming from all sources.

You have 0.3M H⁺ for the strong acid, when H₂S dissociates H⁺ from its dissociation adds up.

[JuniorAAAHAHS]

But isn't that the 0.3M from a different source? why do you still square it?

[Borek]

I already told you:

In Ka you need to account for a total concentration of an ion

Acid (nor any other reacting substance) doesn't know where each ion/molecule it is reacting with comes from, they are all identical, and they all behave identically.

[JuniorAAAHAHS]

Why still square it?

[Borek]

Not sure what your question really is. [H⁺]² is part of the acid dissociation constant definition (actually it doesn't have to be defined, it can be derived from the thermodynamics considerations).