Chapter 11, Problem 11.110PAE

When formic acid is heated, it decomposes to hydrogen and carbon dioxide in a first-order decay:

$\text{HCOOH}\left(g\right)\to {\text{CO}}_2\left(g\right)+{\text{H}}_2\left(g\right)$

The rate of reaction is monitored by measuring the total pressure in the reaction container.

Time (s)

Pressure

(torr) 0 220 50 324 100 379 150 408 200 423 250 431 300 435

Calculate the rate constant and half-life in seconds for the reaction. At the start of the reaction (time = 0), only formic acid is present. (HINT: Find the partial pressure of formic acid using Dalton's law of partial pressure and the reaction stoichiometry to find $P_{\text{HCOOH}}$ at each time.)