Chapter 8, Problem 8G.5E

(a)

Interpretation Introduction

Interpretation:

The volume of nitrogen has to be given.

Concept Introduction:

The volume of nitrogen gas can be find using the ideal gas equation,

  $\text{PV=nRT}$

Where P is the pressure of the gas.

V is the volume of the gas.

R is gas constant $\text{(0}\text{.082057L}\text{atm}{\text{mol}}^{\text{-1}}{\text{k}}^{\text{-1}}\text{)}\text{.}$

T is temperature in Kelvin.

n is the number of moles of the substance.

Answer to Problem 8G.5E

The volume of the nitrogen gas is $\text{0}\text{.35}\text{L}\text{.}$

Explanation of Solution

Given,

The pressure (P) of the gas is $\text{1atm}\text{.}$

The temperature of the gas is $\text{273K}\text{.}$

The mass of the lead azide is 1.5g.

The molar mass of lead azide is 291.24g.

The balanced equation is,

  $\text{Pb}{\left({\text{N}}_{\text{3}}\right)}_{\text{2(s)}}\stackrel{}{\to }{\text{Pb}}_{\left(\text{s}\right)}{\text{+3N}}_{{\text{2}}_{\left(\text{g}\right)}}$

The mass of lead azide is converted to moles as,

  $\frac{\text{Grams}}{\text{1}}\text{×}\frac{\text{1mol}}{\text{Molar}\text{mass}}\text{=moles}$

  $\frac{\text{1}\text{.5 g}}{\text{1}}\text{×}\frac{\text{1mol}}{\text{291}\text{.24 g}}\text{=0}\text{.00515 moles}$

  $\text{Moles}\text{of Lead azide=}\text{0}\text{.00515}\text{moles}$

The volume of nitrogen can be calculated as,

  $\text{PV=nRT}$

  $\text{V=}\frac{\text{nRT}}{\text{P}}$

  $\text{V=}\frac{\left(\text{0}\text{.00515}\text{mol}\right)\left(\text{0}\text{.082057L}\text{atm}{\text{mol}}^{\text{-1}}{\text{K}}^{\text{-1}}\right)\left(\text{273K}\right)}{\text{1}\text{atm}}$

  $\text{V=0}\text{.1153L}$

The volume of one mole nitrogen is $\text{0}\text{.1153L}\text{.}$

The volume for three-moles of nitrogen is $\left(\text{0}\text{.1153×3}\right)=$$\text{0}\text{.35L}\text{.}$

The volume of the nitrogen gas is $\text{0}\text{.35}\text{L}\text{.}$

(b)

Interpretation Introduction

Interpretation:

The volume of nitrogen gas produce by 1.5g of mercury azide is smaller or larger has to be given.

Concept Introduction:

Refer to part (a).

Answer to Problem 8G.5E

The volume of nitrogen produced by mercury azide is larger than the volume of nitrogen produced by lead azide.

Explanation of Solution

Given,

The pressure (P) of the gas is $\text{1atm}\text{.}$

The temperature of the gas is $\text{273K}\text{.}$

The mass of the mercury azide is 1.5g.

The molar mass of mercury azide is 200.59g.

The balanced equation is,

  $\text{Hg}{\left({\text{N}}_{\text{3}}\right)}_{\text{2}}{}_{\left(\text{s}\right)}\stackrel{}{\to }{\text{Hg}}_{\left(\text{s}\right)}{\text{+3N}}_{{\text{2}}_{\left(\text{g}\right)}}$

The mass of mercury is converted to moles as,

  $\frac{\text{Grams}}{\text{1}}\text{×}\frac{\text{1mol}}{\text{Molar}\text{mass}}\text{=moles}$

  $\frac{\text{1}\text{.5}\text{g}}{\text{1}}\text{×}\frac{\text{1mol}}{\text{200}\text{.59}\text{g}}\text{=0}\text{.00748moles}$

  $\text{moles}\text{of mercury azide=}\text{0}\text{.00748}\text{moles}$

The volume of nitrogen can be calculated as,

  $\text{PV=nRT}$

  $\text{V=}\frac{\text{nRT}}{\text{P}}$

  $\text{V=}\frac{\left(\text{0}\text{.00748}\right)\left(\text{0}\text{.082057L}\text{atm}{\text{mol}}^{\text{-1}}{\text{K}}^{\text{-1}}\right)\left(\text{273K}\right)}{\text{1}\text{atm}}$

  $\text{V=0}\text{.1675 L}$

The volume of one mole nitrogen is $\text{0}\text{.1675}\text{L}\text{.}$

The volume for three-moles of nitrogen is $\left(\text{0}\text{.1675×3}\right)=$$\text{0}\text{.50L}\text{.}$

The volume of nitrogen produced by mercury azide is larger than the volume of nitrogen produced by lead azide.

(c)

Interpretation Introduction

Interpretation:

The reason that the metal azide is potent explosives has to be given.

Answer to Problem 8G.5E

The metal azide is potent explosives because azide ion is thermodynamically unstable.

Explanation of Solution

Metal azides are explosive because although the diatomic form of nitrogen is very stable - that is, the triple bond that holds the nitrogen together is very strong and the metal azides themselves are unstable as the bonds between nitrogen atoms and other atoms weak by comparison.  Therefore, little energy is required to overcome these weak bonds, but a great deal of energy is released when the strong triple bond in nitrogen are formed.  The rapidity of the reaction is due to the weakness of the bonds in metal azides and the high quantity of overall energy released is due to the much higher strength of the triple bonds, produce the explosive qualities of these compounds.