Like all equilibrium constants, the value of Kw depends on temperature. At body temperature (37 °C), Kw = 2.4 * 10-14. What are the [H3O+] and pH of pure water at body temperature?

Video transcript

All right. Hi, everyone. So this question says that like all equilibrium constants, the value of KW depends on temperature at body temperature or 37 °C KW is equal to 2.4 multiplied by 10 into the power of negative 14. What are the hydro concentration and Ph of pure water at body temperature? And here we have four different answer. Choices labeled A through D proposing different values for concentrations of hydro num. And Ph now recall that the ionization constant of water or KW refers to an equilibrium for water itself, right? Because recall the two molecules of water can participate in an equilibrium between hydro num that's H 30 positive and hydroxide or O negative. And so KW, which is the corresponding equilibrium constant is the product of the concentrations of both hydro num and hydroxide. Now, there's a very important piece of context provided in this question because the question specifically tells us that pure water is being considered for this problem. Now, because we're given pure water recall that the concentration of hydro num is going to be equal to that of hydroxide. And so because we're only concerned with the concentration of hydro lium. For the context of this question, I can use this relationship to remove hydroxide as a variable. And so KW is equal to the concentration of hydro num multiplied by itself. And so this means that I can write KW as the concentration of hydro num squared. And so after plugging in the value for KW, we can take the square root of that to find the concentration of hydronic. So let's go ahead and do that. In this case, KW is equal to 2.4 multiplied by 10 to the power of negative 14. And that is equal to the concentration of hydro num squared. So to find the concentration of hydro num, I'm going to take the square root of both sides. And so the concentration of hydro num or HVO positive is equal to the square root of 2.4 multiplied by 10 to the power of negative 14. Which after rounding to two significant figures is 1.5 multiplied by 10 to the power of negative seven. So now that we've calculated the concentration of hydro num, we can use this to find the Ph of the solution at body temperature because recall the Ph can be calculated by taking the negative logarithm of the concentration of hydro. In other words, the concentration of acid in your solution. So here Ph is equal to the negative logarithm of 1.5 multiplied by 10 to the power of negative seven. And after I evaluate this expression and round up to two decimal places, I get that the ph of the system or the solution is equal to 6.82. And there you have it. So the concentration of hydro num is equal to 1.5 multiplied by 10 to the power of negative seven. And the ph of pure water at body temperature is equal to 6.82. And this corresponds to option B in the multiple choice and there you have it. So with that being said, thank you so very much for watching and I hope you found this helpful.