1 10 pts The molar mass of phenolphthalein an acidbase indic

1. (10 pts) The molar mass of phenolphthalein, an acid-base indicator, was determined measurements. A student obtained an osmotic pressure of by osmotic pressure 14.6 mm Hg at 25°C for a 2.00 L solution containing 500.0 mg of phenolphthalein. What is the molar mass of phenolphthalein?

Solution

Ans. Given, osmotic pressure, P = 14.6 mm Hg = (14.6 / 760) atm = 0.01921 atm

            Mass of phenolphthalein = 500.0 mg = 0.500 g

# Let the molar mass of phenolphthalein = X g/ mol

So,

            Moles of phenolphthalein = Mass/ Molar mass

                                                            = 0.500 g / (X g / mol)

                                                            = (0.5 / X) mol

Now,

            Molarity of solution = Moles / Volume of solution in liters

                                                = (0.5/ X) mol / 2.0 L

                                                = (0.25/X) M

# Osmotic pressure, P of a solution in given by-

P = i x MRT - equation 1

Where,

i = van’t Hoff factor = 1 for non-ionizing solutes

M = molarity of solution

R = gas constant = 0.0821 atm L mol^-1K^-1 = 0.0821 atm M^-1K^-1

T = temperature in kelvin = (⁰C + 273.05)K

Putting the values in equation 1-

            0.01921 atm = 1 x (0.25/X) M x (0.0821 atm M^-1K^-1) x 298.15 K

            Or, 0.01921 atm = (6.11952875 / X) atm

            Or, X = 6.11952875 atm / 0.01921 atm

            Hence, X = 318.56

Therefore, molar mass of phenolphthalein = X g/ mol = 318.56 g/ mol