So here it says calculate the activity coefficient of calcium ion in 0.25 moller of calcium phosphate. We're gonna have to utilize the Davies equation at some point. But first we need to understand what are ionic strength will be. We're gonna say here ionic strength equals half concentration. One times charge one squared plus concentration two times charge two squared. We're gonna say that this breaks up into three calcium ions plus two phosphate ions. Because there's three calcium ions, it's three times 30.25 molar. Which is gonna give me .075 moller and there's two phosphates. So that's two times .025 moller. Give Me .050 Moller. We're gonna say our ionic strength equals half. So the concentration of calcium ions times the charge squared of calcium plus the charge the concentration of phosphate ions times a charge squared. When we do all that we get an ionic strength of .375 molar. Now with that ionic strength we can plug it into each one of these ionic strengths here We use the charge of calcium ion to find log of our activity coefficient. So log of activity coefficient equals negative .51 plus two squared Times Square root of .375, Divided by one plus .375 Square root of that -3 times .375. So that's gonna equal negative 2.04 Times .612372 Divided by 1.612372 -1125. Then we're gonna say log of our activity coefficient equals negative .545-83. We don't want the log of our activity coefficient. We just want the activity coefficient. So activity coefficient equals 10 to the negative .545283. Which is gonna give me .28 as my activity coefficient. So here, utilizing the equation, we're able to find the activity coefficient of calcium ion Here, these values are just estimates there will be deviations from it if we venture away from mono valent ions. So here are charges plus two. So it's not a valid, it's di valid because it charges to with a charge. So this is how we get this activity coefficient of 0.28. Remember we rely on the Davies equation. If we don't know what the size parameter for the ion is. If we do know the size parameter then we rely on things such as interpolation or the extended huh? Debbie Hucles equation to help us find the activity coefficient for a specified ion. So remember the two equations that extended Debbie Hucles equation. Because when we know what the size parameter is, we can use interpretation as well to help us determine what the activity coefficient is. When size parameters are not known, rely more on the Davies equation
