Calculate the concentration of an aqueous solution of Ca1OH22 that has a pH of 10.05.

Video transcript

hi everyone for this problem. It reads barium hydroxide is an important laboratory. Re agent used for tight rations, calculate the concentration of an acquis barium hydroxide solution. Having a ph of 9.850. So our goal here is to calculate the concentration of barium hydroxide. Okay. And let's remember concentration is malaria t which is moles over leader. In order for us to solve this problem, we're going to need to remember the ion product constant K. W. And K. W. Is equal to our concentration of hydro ni um times our concentration of hydroxide and we know what the value of K. W. Is because this is a constant. So we should have this memorized K. W. Is equal to 1.0 times 10 to the negative 14. So we have K. W. Is equal to our concentration of hydro knee um times our concentration of hydroxide. So now what we need to do is calculate our concentration of hydro knee um and our concentration of hydroxide. And the first one we can start off with is our concentration of hydro knee. Um Okay we can start here because we were given the ph and remember the ph is equal to negative log of hydro knee um concentration. So what that means then is our hydro knee um concentration is going to equal 10 to the negative ph and so we can solve for the concentration of hydro ni um because we know the ph because the ph was given in the problem, we know that the ph is 9.850. So let's plug that in 10 to the negative 9.850 gives us a hydro knee um concentration of 1. times 10 to the negative Moeller. Okay so we just calculated the concentration of hydro ni. Um So now we need to calculate our concentration of hydroxide. Okay so let's rearrange this kW equation so that we're solving for hydroxide. So when we rearrange it we get our concentration of hydroxide is going to equal R. K. W. Which is 1.0 times 10 to the negative over our concentration of hydro ni. Um which we just solved for. So let's go ahead and plug in our concentration of hydro ni. Um 1. times 10 to the negative 10. So now when we solve we get our concentration of hydroxide is 7. times 10 to the negative five molar. Okay so now that we know both our concentration of hydro ni um and hydroxide, how do we calculate the concentration of our age? Barium hydroxide, we're going to need to identify whether or not this is a strong base or a weak base. Okay so barium hydroxide is a strong base. And what that means is it's going to dissociate completely into its ions. Okay so let's visualize that. So barium hydroxide when it dissociates it dissociates into barium ion and hydroxide ion. And we need to calculate the concentration of our barium hydroxide. Alright so because we know our concentration of hydroxide, we can use our multiple ratio between our hydroxide and our barium hydroxide. Okay so let's go ahead and write out or yes we'll write out our concentration of hydroxide that we saw for. So we said that 7. times 10 to the negative five molar. So that's moles of hydroxide over a liter of solution. Now looking at our reaction, we need to look at the multiple ratio. So for every one mole of vary um hydroxide consumed. We have two moles of hydroxide produced. Okay so let's write that in here as a multiple ratio. So for every two moles of hydroxide produced, we have one more. Let's rewrite that one mole of barium hydroxide consumed. Okay so looking at our units here we can see that our moles of hydroxide cancel. And we're left with the units of barium hydroxide over leader which is malaria T. And that's what the question is asking us to solve for the car concentration of Varian hydroxide. So let's go ahead and solve. So when we do this math we get 3.54 times to the negative five molar. So this is our concentration of barium hydroxide. So when we write this as our final answer, our concentration of barium hydroxide is equal to 3.54 times to the negative five. Alright, so this is our final answer, and that is it for this problem. I hope this was helpful.