Question

A 1.0 oz (30.0 mL, 1.00 g/mL) espresso contains 55.0 mg of caffeine (C8H10N4O2). Calculate the caffeine concentration in the following units. You may assume your espresso contains only caffeine and water for simplicity.

a. ppm

b. %w/w

c. ppb

d. Molarity

e. molality

f. Xcaffeine (mole fraction)

Answer 1

espresso is 30 ml and it is 1.0g/ml then

30 ml espresso contain 30 gm espresso that mean 30 gm espresso contain 55 mg caffeine.

a.ppm

55 mg = 0.055 gm

ppm = mass of solute in gm 10⁶/mass of solution in gm

= 0.055 10⁶/30 = 1833.33 ppm

b)%w/w

%w/w = mass of solute in gm 100/mass of solution in gram

= 0.055 100/30 = 0.1833%

ppb = mass of solute in gm 10⁹/mass of solution in gm

= 0.055 10⁹/30 = 1833333.33 ppb

c)molar mass of caffeine = 194.19 g/mol that mean 1 mole of caffeine = 194.19 g then 0.055 gm =

10.055/194.19 = 0.000283 mole of caffine

30 ml = 0.030 L

d)Molarity = no. of mole of solute/volume of solution in liter

= 0.000283 /0.030 = 0.009433 M

e. molality

Molality = no. of mole of solute/mass of solution in kg

= 0.000283mol /0.030kg = 0.009433 m