Chemical explosions are characterized by the instantaneous release of large quantities of hot gases, which set up a shock wave of enormous pressure (up to 700,000 atm) and velocity (up to $20,000 \mathrm{mi} / \mathrm{h})$. For example, explosion of nitroglycerin $\left(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}_{3} \mathrm{O}_{9}\right)$ releases four gases, $\mathbf{A}, \mathbf{B}, \mathbf{C}$
and $\mathbf{D}$
$$
n \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}_{3} \mathrm{O}_{9}(l) \longrightarrow a \mathrm{~A}(g)+b \mathrm{~B}(g)+c \mathrm{C}(g)+d \mathrm{D}(g)
$$
(a) How many moles of hot gas are released by the explosion of $0.00400 \mathrm{~mol}$ of nitroglycerin?
(b) When the products released by explosion of $0.00400 \mathrm{~mol}$ of nitroglycerin were placed in a $500.0 \mathrm{~mL}$ flask and the flask was cooled to $-10^{\circ} \mathrm{C},$ product $\mathrm{A}$ solidified, and the pressure inside the flask was 623 $\mathrm{mm}$ Hg. How many moles of A were present, and what is its likely identity?
(c) When gases $\mathbf{B}, \mathbf{C},$ and $\mathbf{D}$ were passed through a tube of powdered $\mathrm{Li}_{2} \mathrm{O},$ gas $\mathbf{B}$ reacted to form $\mathrm{Li}_{2} \mathrm{CO}_{3} .$ The remaining gases, $\mathrm{C}$ and $\mathrm{D},$ were collected in another $500.0 \mathrm{~mL}$ flask and found to have a pressure of $260 \mathrm{~mm}$ $\mathrm{Hg}$ at $25^{\circ} \mathrm{C} .$ How many moles of $\mathbf{B}$ were present, and what is its likely identity?
(d) When gases $C$ and $D$ were passed through a hot tube of powdered copper, gas $\mathrm{C}$ reacted to form $\mathrm{CuO}$. The remaining gas, $\mathbf{D}$, was collected in a third $500.0 \mathrm{~mL}$ flask and found to have a mass of $0.168 \mathrm{~g}$ and a pressure of $223 \mathrm{~mm} \mathrm{Hg}$ at $25^{\circ} \mathrm{C} .$ How many moles each of $\mathrm{C}$ and $\mathrm{D}$ were present, and what are their likely identities?
(e) Write a balanced equation for the explosion of nitroglycerin.