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Problem 78 Hard Difficulty

A cough syrup contains 5.0$\%$ ethyl alcohol, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},$ by mass. If the density of the solution is 0.9928 $\mathrm{g} / \mathrm{mL}$ , determine the molarity of the alcohol in the cough syrup.

Answer

1.1$M$

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Video Transcript

Yeah, if we have a solution of 5% ethyl alcohol with the density of 0.9928 g per milliliter weaken. You said information to figure out the mill arat e of our solution hilarity. Remember his moles per liter? Yeah. So the first step is to figure out how many moles of well, first step is to figure out the mass of the whole solution. So ethyl alcohol is 46 point 069 grams per mole. NFL alcohol is C two h 50 h. And then we add our water 18.15 g prominent arounds. H 20 That gives us a total of 64 0.84 g. Now, our solution is only 5% ethyl alcohol. So I'm gonna multiply the 64.84 by 0.5 and that gives me 3.20 for 2 g. Now, I'll convert that two moles using the Mueller Mass, and I find that I have 0.70 moles of F full alcohol in my solution. So I'm gonna put that up in my formula now. The next step is to figure out the volume. We don't know what our volume is and so we'll take the mass of the solution 64.84 grams and divided by the density which is 0.9 9 to 8 grams per. Come on later we want leader soul Add this conversion factor toe fix that problem and we get 0.65 leaders. I divide these numbers and I get a mill Arat e have 1.8

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