Write the expression for the ion product constant for water, Kw.

Video transcript

hey everyone today we are being asked to calculate the hydro name ion concentration and the ph of peer water and a temperature of 30 degrees Celsius. Where the ionization constant of water or K. W. Is 1.471 times 10 to the negative 14th. So first things first, the ionization of water States that two moles of water can auto ionized to form one mole of hydro me miles history of plus and one more of oh a child's hey hydroxide and recall that the K. W. The ionization constant is equal to the product of the concentrations of hydro ni um and hydroxide ions present within solution. However, since we're dealing with pure water as mentioned, the question, we can also come to the assumption that the concentration of hydroxide and hydro neem ions should be equal with this in mind. We can go ahead and start solving for the concentration of hydro knee um ions. And to do this, let us just assume or substitute the hydro Nehemiah concentration with a variable, let's use X. So we know that the K. W. Is equal to the product of hydro ni um and hydroxide ion concentrations. But since they're both equal, that means we have X squared substituting the value for K. W. Given in the question stem, We have 1.47, 1 times 10 to the negative 14th 14th is equal to X squared. Therefore to solve for X. The concentration by drowning lions, we can take the square root of both sides. This, sorry, this gives us a final value of 1. .213 Times 10 to the - Moeller. So that is our concentration of hydrogen ions. But we're not done yet, we still need to find the ph. But since we already have the concentration of H three plus ions, this is really simple because recall that ph is equal to the negative log, negative log of the hydro owning my own concentration substituting in the value of X. That we just got. That means it is the negative log of 1.213 Times 10 to the -7 Moller, Which is equal to 6.92. So the concentration of hydro knee um ions in the solution with the kW 1.471 times 10 to the negative 14th was 1.213 times 10 to the 97th mauler And has a ph of 6.92. I hope this helps. And I look forward to seeing you in the next one.