Answer
Please see the work below.
Work Step by Step
We know that
a. The balanced chemical equation for the thermal decomposition of ammonium nitrate can be given as
$NH_4NO_3\rightarrow NO_2+2H_2O$
b. We know that
$PV=nRT$
This can be rearranged as:
$R=\frac{PV}{nT}$
We plug in the known values to obtain:
$R=\frac{0.9947\times 0.340}{0.0128\times 297}=0.08251\frac{L.atm}{mol.K}$
