Question

Question: (a) The energy released in the explosion of 1.00 molof TNT is 340 mJ. The molar mass of TNT is. What weight of TNT is$\mathbf{0}\mathbf{.}\mathbf{227}\mathbf{}\mathit{k}\mathit{J}\mathbf{/}\mathit{m}\mathit{o}\mathit{l}$needed for an explosive release of $\mathbf{1}\mathbf{.}\mathbf{80}\mathbf{\times }{\mathbf{10}}^{\mathbf{14}}\mathbf{}\mathit{J}$? (b) Can you carry that weight in a backpack, or is a truck or train required? (c) Suppose that in an explosion of a fission bomb, 0.080%of the fissionable mass is converted to released energy. What weight of fissionable material is needed for an explosive release of $\mathbf{1}\mathbf{.}\mathbf{80}\mathbf{\times }{\mathbf{10}}^{\mathbf{14}}\mathbf{}\mathit{J}$? (d) Can you carry that weight in a backpack, or is a truck or train required?

Short answer

Answer

1. The weight of the TNT explosive is$1.2\times {10}^{7}kg$ .
2. This amount of weight cannot be carried in a backpack, it would require a train or a truck to carry it.
3. The fission bomb of 2.5 kg would release the same amount of energy.

This bomb could be carried easily in backpack

Step-by-step solution

Given Data

One mol of TNT has a molar mass of $0.227kg$.

Energy released per unit mol$E_{released}=3.40MJ/mol$

Required energy to be released from the bomb is $1.8\times {10}^{14}J$.

Significance of TNT

TNT is still often utilised in the military and, less frequently, in industry. It is a component of many explosives and weapons, including grenades, bombs, and artillery shells. TNT is used in industry to make dyes, photographic chemicals, and for underwater blasting.

Step 3(a): Determine the mass required for TNT bomb.

One mole of TNT releases 340 MJ of energy.

Required energy released in the bomb $1.8\times {10}^{14}J$.

No. of moles required to release this energy is$0.227kg$

$$\begin{gathered} n=\frac{1.8\times {10}^{14}J}{3.40\times {10}^{6}J/Mol} \\ =0.53\times {10}^{8}mol \end{gathered}$$

One mole weight 0.227 kg .

Therefore, $0.53\times {10}^{8}mol$weighs

$\left(0.53\times {10}^{8}mol\right)\left(0.227\frac{kg}{mol}\right)=1.2\times {10}^{7}kg$

Hence the weight of the TNT explosive is $1.2\times {10}^{7}kg$.

Step 3(b): Determination of carry that weight in a backpack, or is a truck or train

The mass of the TNT would be 12 million kilograms which would require a truck or train to carry.

Step 4(c): Determine mass required for fission bomb.

The fission bomb converts 0.080% of mass into energy of$1.8\times {10}^{14}J$ . The mass-energy relation can be used to determine mass required.

$$\begin{gathered} m_o=\frac{E_{rel}}{0.0008c^2} \\ =\frac{1.8\times {10}^{14}J}{0.0008{\left(3\times {10}^8\right)}^2} \\ =2.5kg \end{gathered}$$

Hence the 2.5 kg of fission material is required to release $1.8\times {10}^{14}J$. This weight can be easily carried in a backpack.

Step 5(d): Determination of carry that weight in a backpack, or is a truck or train

The 2.5 kg of fission material is required to release$1.8\times {10}^{14}J$. This weight can be easily carried in a backpack