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Chapter 3: Q78 E (page 172)

A cough syrup contains 5.0% ethyl alcohol C2H5OH, by mass. If the density of the solution is 0.9928 g/ml determine the molarity of alcohol in the cough syrup.

Short Answer

Expert verified

The molarity of alcohol in the cough syrup is 1.08 M.

Step by step solution

01

Step 1- Given data

The density of solution = 0.9928 g/ml.

The cough syrup has a 5% ethyl alcohol by mass.

02

Step 2- Calculating molarity

Let the volume be 1000 ml or 1 L then,

\(\begin{align}mass &= volume \times density\\ &= 0.9928 \times 1000\\ &= 992.8.\end{align}\)

Now, the mass of the alcohol = total mass x 5%

= 0.05 x 992.8 g

=49.64 g.

The number of moles of ethyl alcohol = mass/molar mass

\(\begin{align} &= \frac{{1.08\,{\rm{mol}}}}{{1L}}\\ &= 1.08\;M.\end{align}\)

The molarity = moles/volume

= 1.08/1 l

= 1.08 M.

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