Boiling Point Elevation

[cfive22]

Has anyone ever heard of boiling point elevation that involves an activity coefficient?

∆Tb = kb • i • m • γ

"where ∆Tb is the boiling-point elevation, kb is the boiling-point elevation constant, i is the ionizability constant, m is the molality of the solution, and γ is the activity coefficient of the solute."

This was on TBR CBT 5 and I was unsure how to analyze this.

Based on one of the answers, it states that "The lowest value for γ belongs to the compound that has the least interaction with water."

How were we supposed to know this earlier other than making an assumption?

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[Dasypus]

That activity coefficient is just like the a and b in the van der Waals equation: it's a way of correcting for the fact that real substances don't act like ideal substances. Figuring out what it does in context requires thinking about why boiling-point elevation occurs. First, what's a boiling point? It's when the solvent is hot enough that its vapor pressure is equal to the atmospheric pressure. If you have anything admixed with your solvent, it'll lower the vapor pressure of the solvent slightly. The more it interacts with the solvent, the more the vapor pressure is lowered, because particles of solvent are too busy interacting with that compound to escape as gas. The extra amount you have to heat the solvent to overcome this interaction is the boiling point elevation.

Now, with this in mind, look at the equation they give you. It's got ∆Tb directly proportional to γ. So whatever γ is, if it's 0, then no boiling point elevation, and if it's great, big boiling point elevation. Given what we know about why boiling point elevation happens at all, γ must be a correction for how much the interaction of this particular solute differs from that of the 'ideal' solute.

Did that help at all?

 

[cfive22]

That activity coefficient is just like the a and b in the van der Waals equation: it's a way of correcting for the fact that real substances don't act like ideal substances. Figuring out what it does in context requires thinking about why boiling-point elevation occurs. First, what's a boiling point? It's when the solvent is hot enough that its vapor pressure is equal to the atmospheric pressure. If you have anything admixed with your solvent, it'll lower the vapor pressure of the solvent slightly. The more it interacts with the solvent, the more the vapor pressure is lowered, because particles of solvent are too busy interacting with that compound to escape as gas. The extra amount you have to heat the solvent to overcome this interaction is the boiling point elevation.

Now, with this in mind, look at the equation they give you. It's got ∆Tb directly proportional to γ. So whatever γ is, if it's 0, then no boiling point elevation, and if it's great, big boiling point elevation. Given what we know about why boiling point elevation happens at all, γ must be a correction for how much the interaction of this particular solute differs from that of the 'ideal' solute.

Did that help at all?

This makes a lot of sense. Thanks a lot! Just had never seen the activity coefficient before so wanted to know how to manipulate it. But I guess this is a necessary skill that everyone needs to develop before taking the test because we'll undoubtedly see something that we haven't seen before.

 

[Dasypus]

Glad to help! I hope the sort of reasoning I showed can help you a bit: look at what you already know, and what this weird new thing could be doing, given what happens when you change it.