Chapter 4, Problem 4.19NP

Nitrogen is a vital component of proteins and nucleic acids, and thus is necessary for life, The atmosphere is composed of roughly 80% $N_2$, but most organisms cannot directly utilize $N_2$ for biosynthesis. Bacteria capable of “fixing’ nitrogen (i.e., converting $N_2$ to a chemical form, such as $N{H}_3$, which can be utilized in the biosynthesis of proteins and nucleic acids) are called diazotrophs. The ability of some plants like legumes to fix nitrogen is due to a symbiotic relationship between the plant and nitrogen-fixing bacteria that live in the plant’s roots. Assume that the hypothetical reaction for fixing nitrogen biologically is $N_2\left(g\right)+3H_{2}O\left(l\right)\to 2N{H}_3\left(aq\right)+\frac{3}{2}{O}_2\left(g\right)$

1. Calculate the standard enthalpy change for the biosynthetic fixation of nitrogen at $T=298K$. For $N{H}_3\left(aq\right)$, ammonia dissolved in aqueous solution, $\Delta H_f^{°}=-80.3kJmo{l}^{-1}$
2. In some bacteria, glycine is produced from ammonia by the reaction $N{H}_3\left(g\right)+2C{H}_4\left(g\right)+\frac{5}{2}{O}_2\left(g\right)\to N{H}_{2}C{H}_{2}COOH\left(s\right)+H_{2}O\left(l\right)$
3. Calculate the standard enthalpy change for the synthesis of glycine from ammonia. For glycine, $\Delta H_f^{°}=-537.2kJmo{l}^{-1}$. Assume $T=298K$.
4. Calculate the standard enthalpy change for the synthesis of glycine from nitrogen, oxygen, and methane.