Question

Nitroglycerine ( C3H5N3O9) is a very strong explosive that degrades over time and is too shock sensitive to transport safely. Dynamite is made by combining nitroglycerine with stabilizers and adsorbents, which makes it much safer to use. The explosion of nitroglycerin can be represented by:

4C3H5N3O9(l)→6N2(g)+12CO(g)+10H2O(g)+7O2(g)
A stick of 40% dynamite is about 20 cm long and about 3 cm in diameter and weighs 181 grams. It is 40.0% nitroglycerine by mass. What is the total number of moles of gas produced when a stick of 40% dynamite explodes?

Answer 1

To calculate the total moles of gas produced when a stick of 40% dynamite explodes, first determine the mass of nitroglycerin present in the stick and convert it to moles. Then, use stoichiometry based on the balanced chemical equation for the explosion of nitroglycerin to find the total moles of gas produced, which is approximately 2.79 moles.

Step-by-step explanation:

The total number of moles of gas produced when a stick of 40% dynamite explodes can be calculated by first determining the mass of nitroglycerin in the dynamite. Since the dynamite is 40% nitroglycerin by mass, we can calculate the mass of nitroglycerin as 40% of the 181 grams stick:

Mass of nitroglycerin = 40% × 181 g = 0.40 × 181 g = 72.4 g

Next, we need to find the molar mass of nitroglycerin (C3H5N3O9), which is:

Molar mass of C3H5N3O9 = (3×12.01) + (5×1.01) + (3×14.01) + (9×16.00) = 227.09 g/mol

Number of moles of nitroglycerin = 72.4 g / 227.09 g/mol = 0.319 moles

Total moles of gas produced = (0.319 moles nitroglycerin) × (35 moles gas / 4 moles nitroglycerin) = 2.79 moles of gas

Therefore, when a stick of 40% dynamite explodes, approximately 2.79 moles of gas are produced.

Answer 2

To determine the total number of moles of gases produced when a stick of 40% dynamite explodes, we calculate the mass of nitroglycerin in the dynamite and convert it to moles. With the stoichiometry of the chemical equation for nitroglycerin decomposition, we calculate the moles of gases produced. Approximately 2.80 moles of gases are produced from the explosion of a 40% dynamite stick weighing 181 grams.

Step-by-step explanation:

When a stick of 40% dynamite explodes, the major component, nitroglycerin, decomposes rapidly in an exothermic reaction, producing gaseous products that contribute to the blast. The chemical equation representing the decomposition of nitroglycerin is given by:
4C3H5N3O9(l) → 6N2(g) + 12CO(g) + 10H2O(g) + 7O2(g).

To calculate the total number of moles of gas produced, we first need to find the mass of nitroglycerin in the stick of dynamite. Given that the dynamite is 40.0% nitroglycerin by mass and the entire stick weighs 181 grams, we can calculate the mass of nitroglycerin as follows: 181 grams * 0.40 = 72.4 grams.

Next, we need to convert this mass to moles using the molecular weight of nitroglycerin, which is 227 grams/mole (C3H5N3O9). Thus, the moles of nitroglycerin are: 72.4 grams / 227 grams/mole = 0.319 moles. According to the stoichiometry of the balanced equation, 4 moles of nitroglycerin produce a total of 35 moles of gases (6 moles of N2, 12 moles of CO, 10 moles of H2O, and 7 moles of O2). So we can calculate the total moles of gases produced from 0.319 moles of nitroglycerin as follows:

MoIes of gases = 0.319 moles nitroglycerin * (35 moles gases / 4 moles nitroglycerin) = 2.80375 moles of gases.

Therefore, the total number of moles of gases produced when a stick of 40% dynamite explodes is approximately 2.80 moles.