There’s actually much more in seawater than just dissolved NaCl. ...

Question

There’s actually much more in seawater than just dissolved NaCl. Major ions present include 19,000 ppm Cl-, 10,500 ppm Na+, 2650 ppm SO 2-, 1350 ppm Mg2+, 400 ppm Ca2+, 380 ppm K+, 140 ppm HCO3-, and 65 ppm Br-.
(a) What is the total molality of all ions present in seawater?

Accepted Answer

Hello everyone on this problem we're analyzing a sample of lake water that was found and it contains all these different concentrations of different ions including potassium sodium and so on. So in this problem trying to calculate the total morality of these ions in the lake. So let's remember that the units of PPM which is a unit of concentration is equal to the mass of our salute over the mass of the solution times 10 to the six. Alright so first thing we can do is assume that we have 1000 g of our solution. So gamble assuming We have 1000 g of solution. So here I'm gonna go ahead and make a little table so we keep track of all the ions and the mass and the molds. So here we'll have ions. Then we can go ahead and do mass and then the last one we can do moles. So for ions we have K plus and a plus MG two plus cl minus C two plus. I'll just scroll down here extending these here a little bit. Okay, continue on with S. 042 minus and H C. 03 minus. So from us how can calculate this is dividing the given concentration of PPM units over 1000. Again we're just following this year. Alright so for K. Plus then we've seen the problem that we're given 255 PPM of K. Plus we divide that by 2000 and then we get the value of 0.255 units being grounds. And now for moles so this again is our mass And then for moles we can just do it here again. Let's do R K. Plus an example. So we start off the dimension analysis with 0.255 g. So we'll just calculate for for a mass they will go ahead and use the molecular weight of the elements. So for every one mole of potassium will get 39.983 g. See then that our grams unit will cancel Which gives us a more value of 6.5-2 times 10 to the -3 moles. So that's what I'll go ahead and plug in to 6.5 to times 10 to the negative three. So the same exact thing here and here we'll do for the other ions with the given amount of concentration of the ions. So I won't work this out. But these are the values that you should be getting. So for our sodium we should get 7.6 g moles being 0.3306. Again these units for moles of course just moles. Alright continue on to Magnesium. So we have 1.2 g moles being 0.04197. Now for chlorine we have the mass being eight or 13. Sorry 13.8 grounds and then moles being 0.3893. Then for calcium we have zero 214 g And then the moles being 5.340 times to the -3 moles. Now for our poly atomic and ions we have so far to minus the mass of that is 1.9. And for our moles we have 0.01978. Our last eye on here, we have the mass being zero points to 89 And the moles being 4.73, 6 times 10 to the -3 moles. All right, So I'll go ahead and scroll down for more space here. So now we can go ahead and calculate the total mass of our ion. So basically we're swimming up everything that we calculate for here. So the total mass of our ions, if I just sum up everything in that row or column, we get the sum of 25.78 g. Now for the total moles of ions again to summon up everything here We get the sum of 0.7, 0.7982. And units being moles. So now calculate for the mass of water. So the mass of H 20. We have 1000 minus 25.78 g which gives us a difference of 974. g will convert this into kilograms. Because we want to calculate for the morality. So one kg on top and 1000 g on the bottom, we see that the g unit will cancel. So here we get the value of 0.9749-2 units being kg. Now, finally, we have all the tools that we can go ahead and calculate for the morality, so that's represented as a lower case. M So then we have the moles on top being 0.7982, And then denominator will be our kg, which we just calculated for is 0.9749-2. So putting this into my calculator, I get the morality of 0.819. So this right here is going to be my final answer for this problem.

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