At \$25^circ mathrmC,\$ a saturated solution of benzoic acid \$left(K_mathrma=6.4 imes 10^-5 ight)\$ has actually a pH of \$2.80 .\$ Calculate the water solubility of benzoic acid in moles per liter.

You are watching: The acid-dissociation constant for benzoic acid (c6h5cooh) is 6.3×10−5. ### Video Transcript

this question here is actually a lot user than it appears. On initially glance, um, were given a k a about you for on Acid. I think it's Ben's OIC acid, which is equal to 6.4 times 10 to the negative fifth, and we're told that it has a pH of 2.8. And now, once we were asked to number out Is the soluble ity off benzo actors in water? And we could be thinking choose exactly how just how in the human being we're gonna use this information to acquire there And really, we just It's all in the one key work-related that the benzoate acid is saturated, definition that no even more benzoate acid can be added. That would disfix in water. And so, basically what we have is we have actually the maximum concentration of benzoate acid, bring about a ph of 2.8, and we're told what the pay is. And so all we have to perform is use the K, use the pH and number out what that concentration is of benzo gas and also because it's a saturated solution via, That's the answer we're looking for in terms of what is the soluble ity off Benzo asked water. And so we're gonna rewrite que as the mass action expression, which is going to be HBO plus times the concentration of I'll just speak to it Ben minus for the, uh, for Benzia. I'm not sure what the precise term would be, but we'll simply say H ban is for Ben's OIC acid. And so, if you perform a nice table for this reactivity, you'll uncover, prefer constantly that the outcome would be equal to X square over the initial concentration of H. Benn's minus X, where X is equal to the concentration of HBO plus, which is falsely, easily confiscate concentration of the congregate base. Now, if you understand, if you don't think this, go ahead to the ice table positivity on. Convince yourself that this is true. Now we actually know what X is here, and bereason we know the concentration of HBO plus not straight but because we know the pH. We usage the relationship that the contrails from HBO plus equal to 10 through the negative pH, which in this situation is 2.8, and also if you put it right into the calculator, you'll acquire that this is equal to 1.58 times tense. A aboriginal 3rd Moeller, which here we labeled us access currently that below. And so really we have actually k this was provided to us. It's that 6.4 time to 10th the negative. Fifth, we have actually X. Now we're searching for this value.

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I'm simply gonna plug and also 2 o'clock later, it's simply some straightforward algebra, and also we'll get that. That concentration initially is equal to 0.408 Moeller in that stance or look.