Question #e3ea3

1 Answer
Nathan L.
May 25, 2017

(d) #101.5^oC#

Explanation:

We can automatically eliminate options (a) and (b), because one of the colligative properties of solutions is boiling-point elevation, meaning the boiling point will have increased (i.e. greater than #100.0 ^oC#).

The equation for calculating boiling-point elevation is

#DeltaT_"b" = i * K_"b" * m#

where #DeltaT_"b"# is the change in boiling point,
#i# is called the van't Hoff factor, which for these purposes is essentially the number of dissolved species in one unit of solute (equal to #2# for #"NaCl"#),
#K_"b"# is the molal boiling-point constant for water, which is given, and
#m# is the molality of the solution.

Plugging in our known variables, we have

#DeltaT_"b" = (2)(0.512( "^oC)/cancel(m))(1.5cancel(m)) = 1.5 ^oC#

To find the new boiling point, simply add this to the boiling point of water, #100 ^oC#:

#100 ^oC + 1.5 ^oC = color(red)(101.5 ^oC#

So option (d) is the correct answer.

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