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Is it possible for a solution to have $\left[\mathrm{H}^{+}\right]=0.002 \mathrm{M}$ and $\left[\mathrm{OH}^{-}\right]=5.2 \times 10^{-6} \mathrm{M}$ at $25^{\circ} \mathrm{C}$ ? Explain.

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Numerade Educator

Drexel University

University of Maryland - University College

University of Toronto

it's This will be a quick review on doing calculations using the auto ionization constant off water I've written on the left side of the equation here. It's all from Representatives Case of W. So this value is a constant, actually delivery and constant. So it is unit list, and it actually varies depending on the temperature of the solution that we're talking about. So usually we're working with things at around room temperature, which is around 25 degrees Celsius. And at this temperature, this Constance equal to 1.0 times 10 to the negative 14. So this the fixed quantity at this temperature, this doesn't change, so you can see from the right side of the equation here. This is equal to the product of the concentration of the hydrogen ions, or protons and solution and the concentration of the hydroxide ions in solution. And just remember, when we're writing these quantities and brackets, we're talking about their concentration in terms of, um, polarity. So moles per liter. So we can have essentially any values of either of these as long as their product equals this value here at 1.0 times sent to the negative 14 On these, I use air going to change the concentrations or other of each or other. Increase your decrease depending on the pH. Um, so we can determine some allowed values as long as these add up properly. So if we're talking about a solution with a ph of seven, we know that this is a neutral solution so that the amount of the protons and the hydroxide ions in solution are equal. So in each case, they're the same, so they must have a concentration of 1.0 times 10 to the 2nd 7th Moeller Native seventh story, maybe the seventh more. If we were to multiply these values against one another, we would get this 1.0 times sent to the negative 14th. So, given a set of die use, we can determine whether it's valid or not using this equation. So let's say that we had in a hypothetical situation we think that we have a concentration of protons of 0.2 Moeller and we think that we have a concentration for the hydroxide ion sir O H minus here as 5.2 times 10 to the negative six Mohler So how can we determine whether or not these air diet ballot concentrations? So we already know that we have this expression written here. We can just multiply these two values together because the k double she kw, she equal the product of the two. So if we do that, it comes out to around 1.0 times 10 it's a negative. So now all we need to dio is check that against the value for this case of w constant, which is 1.0 times since the negative 14th. So these values are not equal. So this must not be a valid combination for these two concentrations here. So these are measurements that were taken for the solution. This should give you sort of a red flag that maybe something was done incorrectly here because this is not