 Okay, so if we want to understand how non-ideal, if we want to be able to measure how non-ideal a solution is, we need to use something other than the activity. Just as a reminder of what I'm summarizing here, we've got for ideal solutions, partial pressure is linearly proportional to the mole fraction, so this is the mole fraction axis, here's the Raoult's law behavior, and we have different behaviors for a solution that exhibits positive or negative deviations from Raoult's law, any of which we can capture with this equation that just says the partial pressure is the activity multiplied by the vapor pressure rather than the mole fraction multiplied by the vapor pressure. In the specific case of an ideal solution, the activity of an ideal solution is equal to its mole fraction, and we recover the ideal case. So for example, if I say a particular solution has an activity, or the solvent A in a particular solution has an activity of 0.6, to stick with that example, what I'm saying is if the Raoult's law solution has a partial pressure of this value at a mole fraction of 0.6, if my system has positive deviations from Raoult's law, when it has the same partial pressure of A as the Raoult's law solution has at a mole fraction of 0.6, this non-ideal solution has a different mole fraction, so this value of the mole fraction, a non-ideal solution with let's say 0.5 mole fraction of A has the same partial pressure as the ideal solution would have had at a mole fraction of 0.6, because the solvent A is more active in this solution than we'd have predicted just from Raoult's law. Likewise, if we have negative deviations, maybe we need a mole fraction of 0.65 or 0.7 to have this partial pressure, which is the same as the ideal Raoult's law solution would have had with the mole fraction of 0.6. That's what activity means. Often, we'd rather intuitively just think about, OK, am I above or am I below? Am I exhibiting positive deviations or negative deviations? That's a more intuitive way to think about how the solution is behaving rather than the mole fraction that the ideal solution would have had to have. So often, what we talk about instead is not the activity, but the activity coefficient. So if I take the activity divided by the mole fraction, so again, I'm defining this quantity, remember, in a perfectly ideal solution, the activity and the mole fraction are the same. The activity is the same as the mole fraction if the solution behaves ideally. In a system with positive deviations, the activity is going to be greater than the mole fraction. In a system with negative, because the partial pressure is greater than we'd expect, in a system with negative deviations, the activity is lower than the mole fraction. So I can use this ratio of the activity to the mole fraction to define how ideal the solution is. That activity coefficient will be exactly equal to one in the ideal case. So that's the activity coefficient. In the ideal case, the activity coefficient is equal to one. In the non-ideal case, the activity coefficient is less than one if we exhibit negative deviations from Reld's law or the activity coefficient is bigger than one if we're exhibiting positive deviations from Reld's law. So that's usually an easier way to think about what's going on. If I tell you the activity coefficient is 1.1, then you know immediately the activity is 10% higher than it would have been if the solution is ideal. So that's usually a nice way to think about how non-ideal the solution is, to think about the activity coefficient directly. So let's work an example to make sure these ideas are relatively clear. So let's say we have this system that we've used as an example before, a solution of acetone and chloroform. So that will exhibit negative deviations from ideality from Reld's law because the hydrogen bonding between the acetone and the chloroform. And let's say we use some experimental data. If we prepare a solution, a 60-40 solution, so 60% mole fraction acetone as a mole fraction, 40% chloroform, we can measure the partial pressures of the two substances above that solution. The partial pressure of acetone at 35 degrees Celsius will be 190 Torr. Partial pressure of chloroform will be 80 Torr. And those can be compared to the vapor pressures for pure acetone as a solvent. Pure acetone has a vapor pressure of 350 Torr at this temperature. Chloroform at a temperature of 35 Celsius has a vapor pressure of 300 Torr. So those two numbers we can look up, we can certainly measure them of course. These partial pressures measured at 35 degrees Celsius are particular to that particular preparation of a solution. The question then is what are the activities of the two different solvents in this solution and what are their activity coefficients and how do we interpret those values? So activities of acetone and chloroform, activity coefficients of acetone and chloroform, what are those four values? So we can use our various definitions to obtain those. The activity is the ratio of a partial pressure to a vapor pressure. So the activity of acetone is its partial pressure over its vapor pressure. In this case that's 190 Torr over 350, which works out to be 0.54. Okay, so there's a numerical result. The activity of acetone is 0.54 in the solution. What does that mean? How do we interpret that number? Remember activity just tells us this solution is behaving as if it had a mole fraction of 0.54 acetone. Behaving it like an ideal solution would behave if its mole fraction was 0.54. Its mole fraction is actually 0.6, not 0.54. So that number is lower than this number. The solution is less, the acetone is less active than we would expect for a solution with mole fraction 0.6. Likewise for chloroform, we can take the ratio of partial pressure to vapor pressure, partial pressure of 80, vapor pressure of 300. So 80 divided by 300, that gives us 0.27. So again, the chloroform in the solution behaves as if it were in an ideal solution with mole fraction 0.27. It actually has mole fraction 0.4, but if we want to continue using Raoult's law, we have to pretend that it has a mole fraction of 0.27. That's what this equation is. Now that we have those activities, we can calculate the activity coefficients. Activity coefficient of acetone being its activity divided by its mole fraction. Activity of 0.54 divided by a mole fraction of 0.6. So 0.54 is 90 percent of 0.6. So that's the number that tells us acetone is only 90 percent as active as it would be in an ideal solution. So the activity coefficient is 0.9. It's only 0.9 as active. So now we know confirming what we expected would be true about acetone and chloroform, that this is a system that exhibits negative deviations from Raoult's law. The partial pressure is lower than Raoult's law would predict the activity coefficient is less than one, which means the same thing is saying the activity is less than the mole fraction. Similarly for chloroform, if I take the activity of chloroform over its mole fraction, activity of 0.27 divided by mole fraction of 0.4, that is two-thirds. Again, that value is less than one, meaning that chloroform is also less active than Raoult's law would predict in this solution. It's exhibiting negative deviations from ideality. So both of these solvents have their partial pressures depressed by the existence of the other one. Notice that these two numbers are not equal. There's no reason they should be equal. What this means is that chloroform is more non-ideal in this case than acetone is. Chloroform has its partial pressure reduced more by the presence of acetone than acetone has its reduced by chloroform. The deviation from the ideal case is larger for chloroform than acetone. Acetone has a stronger effect on chloroform than chloroform has on acetone. Okay, so that's the summary of the activity coefficient, which as I've said is maybe a more intuitive way to think about how a solution is behaving non-ideally, how non-ideal it is, as well as some examples of the relatively simple arithmetic that we use to determine activities and activity coefficients.