Calculate the mass (in g) of sodium chloride needed to prepare500 mL solution with a concentration of 3.00 M....

What volume, in $\mathrm{mL}$, of $2.50 \mathrm{M}$ of sodium chloride solution is needed to obtain $3.0 \mathrm{~g}$ of $\mathrm{NaCl}$ by evaporation? (9.4)

Okay, This is called 16 from chapter 15 and asking to calculate the mass of each salute in a 285 grams of solution. So that give us the percent the mass percent and they give us the grants. Absolution. So what we all celebrate full solving for in this equation is the grandson stop. So, essentially, to get that, you're gonna have to convert the percent to a decimal, and you do that by by and by 100. And once you get the decimal, you moved in quite grand situation to find the cramp assaulted. So the graphs of solution that give us in here is 285 Gramps. Okay, so a says there's there's a 5% mass of salt, so we have to convert that 5% into a decimal, which is zero 0.5 now. Since we have 205 grams of solution, you times that by the to 85 and that is going to give you 14 0.3 grams of this salt solid. So in a CEO. Okay, now be has 7.5% math of any two CEOs. Are you? So once again. The 7.5% is going to be converted and two is a small making it point zero seven five. And we still have a to 85 grams of solution. Simple. Deploy that by the to 85 and that is going to come out to 21. All right, for grams of the in A to I see oh three.

The question is asking what mass of each Salyut. So an a C L in n two c 03 is present in a 285 grams solution that contains 5% by mass of N A. C l and 7.5% by mass of N two c 03 So I've written out what we're given. So that's all right in here. And I've also written out to feed percent mass formula, which is equal to mass of the soul Ute divided by the total mass of the solution, which is this to 85 grams here, uh, multiplied by 100. So we're given the percent mass for each of these soul Eudes here and here. So we are trying to solve for the mass of the Salyut. So first, let's find the mass of an A C l, which is our first saw you. So I'm just gonna write in what we have into the formula. So 5% and we're looking for massive the salutes that's are unknown. I'm just going to write X as our unknown variable and divided by mass of the solution, which is to 85 grams this is all multiplied by 100. So in order to work backwards and solve for this X, we have to divide both sides by 100 as this number was multiplied by 100. So if we divide both sides, this will cancel out and five divided by 100 gives us zero point 05 equals X over to any five grams. We rearrange the equation you can solve for X so X is equal to 0.5 multiplied by 200 and 85 grams and this is equal to 14 way to five grams. So now we can solve for the mass of end to see 03 Also Sorry. Go back to this number. We can around this to 14. 23 grams. Okay, Now, to solve for the mass of end To see 03 you do the same thing. So you feeling when we have you have 7.5 0% by mass, which is equal to mass of into CEO three, which we're gonna replace with X, the unknown variable divided by massive a solution which is to 85 grams times 100 and again we're gonna divide both sides by 100 toe isolate for X. Get rid of this term. Did I buy 100? And this gives us zero point 075 which is equal to X over to 85 grams. And again we can rearrange for X, which is equal to zero point 075 well supplied by Teoh 85 grams and this gives us 21 point 375 grams, which we can round two 21.4 grams. So these are our two answers. This is the mass of N A C l. And this is the math, uh, and to see oh, free.

Okay, so we need to calculate the number of sodium ions in 25. Or starting a mountain is 25 grams of sodium chloride. So in order to do that, um, we are gonna need a molar mass right here. So we need to get into moles. I always get in the malls. Whenever we start with grams or anything else, get into moles, and then you can go anywhere from there. So I need the molar mass, so I'm gonna add one sodium 22.990 in one. Chlorine 35.45 for my molar mass. So that will be 58 point for three grams on the bottom there. So that's gonna let me cancel out my unit, grams. So now I'm left with moles. Miles is not what I'm looking for. I'm looking for sodium ions. So, um, I need to cancel out moles of an A C. L. And I know in one mole of an a C. L. There's actually one mole of courting ions. Three kids are animals. So, um, that's great and dandy, But I don't want moles. I want actual ion. So now I'm gonna multiply by avocados number. Look, not chloride ions were looking for sodium. So let's fix that real quick. So I'm sure. Ah, any of you are very confused. I'm sorry about that, huh? Luckily, it was a 1 to 1 ratio. So kids love my moles, then we'll multiply across. So 25 times one divided by 58.443 times one divided by one time, 6.2 times in the 23rd divide by one, we end up with 2.5 eight times 10 the 23rd ah sodium iam's.

If you recognize what to do, this is pretty much just a conversion calculation. We'll start with our middle leaders, converted toe leaders. When we have leaders, we can now use Mill Arat. AEA's a conversion factor to go from leaders. Two moles by multiplying by the polarity. Then we have moles. We can convert the moles into grams by multiplying by the Moeller math. So there are 2.7 g and a C. L and 35 mil leaders of the solution.