Question

With reference to the "Chemistry Put to Work" box on explosives, (a) use bond enthalpies to estimate the enthalpy change for the explosion of \(1.00 \mathrm{~g}\) of nitroglycerin. (b) Write a balanced equation for the decomposition of TNT. Assume that, upon explosion, TNT decomposes into \(\mathrm{N}_{2}(g), \mathrm{CO}_{2}(g)\), \(\mathrm{H}_{2} \mathrm{O}(g),\) and \(\mathrm{C}(s)\)

Short answer

(a) The enthalpy change for the explosion of 1 g of nitroglycerin is -13.058 kJ. (b) The balanced equation for the decomposition of TNT is: \[ 2\text{C}_7\text{H}_5\text{N}_3\text{O}_6 \longrightarrow 3\text{N}_{2}(g) + 7\text{CO}_{2}(g) + 5\text{H}_{2}\text{O}(g) + 7\text{C}(s) \]

Step-by-step solution

Find the molecular formula of nitroglycerin

Nitroglycerin has a molecular formula of C3H5N3O9.

Calculate the number of moles of nitroglycerin

To find the number of moles, we need to divide the mass by the molar mass of nitroglycerin. Molar mass of nitroglycerin: (3 × 12.01) + (5 × 1.01) + (3 × 14.01) + (9 × 16) = 36.03 + 5.05 + 42.03 + 144 = 227.11 g/mol Number of moles: 1 g / 227.11 g/mol = 0.0044 mol

Write the balanced equation for the decomposition of nitroglycerin

\[ 2\text{C}_3\text{H}_5\text{N}_3\text{O}_9 \longrightarrow 6\text{CO}_2 + 10\text{H}_2\text{O} + 6\text{N}_2 + \text{O}_2 \]

Calculate the energy changes using bond enthalpies

We need to break all the bonds in the reactants (nitroglycerin) and form new bonds for the products. The bond enthalpies will be used for these calculations. ΔH = Σ(Bond enthalpy of bonds broken) - Σ(Bond enthalpy of bonds formed) The bond enthalpies we need are: C-H: 413 kJ/mol, C-N: 305 kJ/mol, N-O: 201 kJ/mol, C-O: 358 kJ/mol C=O: 799 kJ/mol, O-H: 463 kJ/mol, N≡N: 945 kJ/mol, O=O: 498 kJ/mol For the reaction equation, we have: 1 nitroglycerin molecule: - Break 3 C-H bonds, 3 C-N bonds, 6 N-O bonds, and 3 C-O bonds. - Form 6 C=O bonds, 5 O-H bonds Therefore, for 2 nitroglycerin molecules, we need to multiply the bond enthalpies by 2. ΔH = [2 × (3 × 413 + 3 × 305 + 6 × 201 + 3 × 358) - 2 × (6 × 799 + 10 × 463 + 6 × 945 + 498)] kJ/mol ΔH = -2970 kJ/mol

Calculate the energy change for the explosion of 1 g of nitroglycerin

Use the moles (0.0044 mol) calculated in step 2: ΔH (1 g) = ΔH (1 mol) × moles ΔH (1 g) = -2970 kJ/mol × 0.0044 mol = -13.058 kJ The enthalpy change for the explosion of 1 g of nitroglycerin is -13.058 kJ. b) Write a balanced equation for the decomposition of TNT

Find the molecular formula of TNT

TNT (trinitrotoluene) has a molecular formula of C7H5N3O6.

Write the decomposition equation

The decomposition products are: N2(g), CO2(g), H2O(g), and C(s). From the 3 nitrogen atoms present in one TNT molecule, 1.5 N2 molecules are formed. The carbon atoms form CO2 and C(s) and hydrogen form H2O in an explosive reaction. To produce the minimum number of whole molecules in the products, we can assume that 2 moles of TNT form the products. \[ 2\text{C}_7\text{H}_5\text{N}_3\text{O}_6 \longrightarrow 3\text{N}_2 + 7\text{CO}_2 + 5\text{H}_2\text{O} + 7\text{C}(s) \] The balanced equation for the decomposition of TNT is: \[ 2\text{C}_7\text{H}_5\text{N}_3\text{O}_6 \longrightarrow 3\text{N}_{2}(g) + 7\text{CO}_{2}(g) + 5\text{H}_{2}\text{O}(g) + 7\text{C}(s) \]

Key concepts

Bond Enthalpies

In chemistry, bond enthalpies (or bond dissociation energies) are fundamental to understanding the energy changes that occur during chemical reactions. They represent the energy required to break a specific type of chemical bond in a molecule in the gaseous state. Essentially, you can think of bond enthalpies as the 'strength' of a bond - the higher the value, the stronger the bond.

When a chemical reaction occurs, bonds in the reactants must be broken and new bonds in the products are formed. The difference between the energy needed to break bonds and the energy released from forming bonds is known as the enthalpy change (ΔH). This is calculated using the formula:
ΔH = Σ(Bond enthalpies of bonds broken) - Σ(Bond enthalpies of bonds formed)

It's important to note that the enthalpy change for a reaction is a crucial factor in determining the spontaneity and conditions required for a reaction to proceed. If the value of ΔH is negative, the reaction is exothermic, releasing energy to the surroundings. Conversely, a positive ΔH indicates an endothermic reaction, absorbing energy.

Explosion Chemistry

The branch of explosion chemistry is concerned with rapid, high-energy chemical reactions that produce an explosion. These reactions are characterized by a sudden release of heat and gas, resulting in a rapid expansion of volume and a release of a large amount of energy in a very short time.

Explosives such as TNT or nitroglycerin rapidly decompose into simpler substances, causing a shock wave through the production of gas at high temperature and pressure. The bond enthalpies of the molecules participating in the reaction are crucial to understanding the amount of energy released during such an explosive reaction.

Molecular Decomposition in Explosions

Explosive materials undergo a rapid molecular decomposition, which results in the breaking of chemical bonds within the compound. This process releases a significant amount of energy that, in the case of nitroglycerin, is mainly due to the formation of stable gaseous products like CO_2 and N_2, which are prevalent in the explosion chemistry.

Molecular Decomposition

Molecular decomposition refers to the breaking down of complex molecules into simpler substances, often involving the breaking of chemical bonds. For explosive reactions, this process must be swift and exothermic to result in an explosion. Decomposition can happen through various mechanisms depending on the nature of the material and the conditions of the reaction.

In the case of nitroglycerin, the process of molecular decomposition releases gases in a very rapid manner and is the central event in the explosion. Each chemical bond breakdown and the following transformation into stable molecules is guided by the bond enthalpies associated with each specific bond in the molecules involved.

The balanced chemical equation for the decomposition provides insight into the stoichiometry and proportion of starting materials to products, essential for calculating energy changes accurately.

Balanced Chemical Equations

Every chemical reaction can be represented by a balanced chemical equation, highlighting the principle of mass conservation. This means that the number of atoms for each element must be the same on both the reactants and products side of the equation. Balancing chemical equations is a fundamental step in the study of chemistry as it gives a clear picture of the substances involved in a reaction and their quantitative relationships.

When dealing with explosives like nitroglycerin or TNT, writing a balanced chemical equation for their decomposition helps to quantify the energy change associated with the explosion. It also helps understand the molar ratio in which the reactants react to form products, this is vital for calculating the molar enthalpies and predicting the amounts of heat and gases released by the explosion. The balanced equation for TNT's decomposition in the exercise demonstrates the direct relationship between the reactants and their respective gaseous and solid products.