Chapter 20, Problem 23E

Acetoacetic acid, ${\text{CH}}_{\text{2}}{\text{COOH}}_{\text{2}}\text{COOH}$ , a reagent in organic synthesis, decomposes in acidic solution, producing acetone and ${\text{CO}}_{\text{2}}\left(\text{g}\right)$ .

   ${\text{CH}}_3{\text{COCH}}_2\left(\text{aq}\right)\to {\text{CH}}_{\text{3}}{\text{COCH}}_{\text{3}}\left(\text{aq}\right){\text{+CO}}_{\text{2}}\left(\text{g}\right)$

The first-order decomposition has a half-life of 144 min.

1. How long will it take for a sample of acetoacetic acid to be 65% decomposed?
2. How many liters of CO₂ $24.5°\text{C}$₇₄₈Torr, are produced as a 10.0 g sample of ${\text{CH}}_{\text{2}}{\text{COCH}}_{\text{2}}\text{COOH}$ decomposes for 575 min? ]lgnore the aqueous solubility of ${\text{CO}}_{\text{2}}\left(\text{g}\right)$ .]