Final answer:
To calculate the volume of acetic anhydride required, determine the mass of water in 17 ml of 72% perchloric acid, convert this to moles of water, and use stoichiometry given the reaction with acetic anhydride to find the moles (and thus mass) of acetic anhydride needed. Then, using the density of acetic anhydride, compute the volume required.
Step-by-step explanation:
The question is asking us to calculate the volume of acetic anhydride required to react completely with the water present in 17 ml of concentrated perchloric acid, given the specific gravities of perchloric acid and acetic anhydride. To find this, first, we need to calculate the mass of water in the 17 ml of perchloric acid. We are given that the solution is 72% perchloric acid by mass. The mass of perchloric acid is 17 ml × 1.60 g/ml = 27.2 g. The mass of water is therefore 28% of this mass, which is 0.28 × 27.2 g = 7.616 g.
To determine the mole fraction and moles of water, we use the molar mass of water (18.015 g/mol). Thus, moles of water = 7.616 g / 18.015 g/mol = 0.423 moles. Acetic anhydride reacts with water in a 1:1 molar ratio to produce acetic acid and acetic anhydride. Therefore, 0.423 moles of acetic anhydride are needed. With the density of acetic anhydride being 1.02 g/ml, we can now find the volume required: mass = moles × molar mass (with molar mass of acetic anhydride being approximately 102.09 g/mol), which gives us the mass of acetic anhydride as 0.423 moles × 102.09 g/mol = 43.183 g. Finally, volume = mass / density = 43.183 g / 1.02 g/ml = 42.33 ml of acetic anhydride is needed to react with the water in the perchloric acid solution.