How do I solve this problem? "if concentrated acetic acid is 12M, then what is the molarity of 100 mL of vinegar (5% solution)? show work."

1 Answer
Truong-Son N.
Jun 5, 2018

The volume is irrelevant. I get #"0.874 M"#. And it seems like #"12 M"# acetic acid is #68.6%"w/w"#. That makes sense because actual concentrated acetic acid is #99.5%"w/w"# and is #"17.4 M"#:

#(68.6%)/(99.5%) xx "17.4 M" ~~ "12 M"#

Given a percent of solution, it is generally assumed to be percent by mass, i.e. #"% w/w"#. The density of vinegar on the average is #"1.05 g/mL"#.

It is convenient to choose a #"100 g"# sample, so that

#5%"w/w" = ("5 g acetic acid")/("100 g vinegar")#

Therefore:

#5 cancel"g acetic acid" xx "1 mol"/(60.05 cancel"g") = "0.0833 mols acetic acid"#

From the density of the solution, we can find the volume it would have.

#100 cancel"g vinegar" xx "1 mL"/(1.05 cancel"g") = "95.24 mL"#

#=# #"0.09524 L vinegar"#

Therefore, the molarity is:

#color(blue)(["acetic acid"]) = "0.0833 mols acetic acid"/"0.09524 L vinegar"#

#=# #color(blue)("0.874 M")#

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