Detonation of nitroglycerin proceeds as follows: 4 C3H5N3O91l2¡ 12 CO21g2 + 6 N21g2 + O21g2 + 10 H2O1g2 (a) If a sample containing 2.00 mL of nitroglycerin 1density = 1.592 g>mL2 is detonated, how many moles of gas are produced?

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Calculate the mass of nitroglycerin using its volume and density: \( \text{mass} = \text{volume} \times \text{density} \).

Convert the mass of nitroglycerin to moles using its molar mass: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \).

Use the balanced chemical equation to determine the mole ratio between nitroglycerin and the total moles of gas produced.

Calculate the total moles of gas produced by multiplying the moles of nitroglycerin by the mole ratio from the balanced equation.

Sum the moles of each gas product (CO2, N2, O2, H2O) to find the total moles of gas produced.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows us to calculate the amount of substances consumed and produced in a reaction based on balanced chemical equations. In this case, understanding the stoichiometric coefficients from the balanced equation for nitroglycerin detonation is essential to determine the moles of gas produced.

Molar Mass and Density

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). Density, defined as mass per unit volume, is crucial for converting the volume of a liquid (in this case, nitroglycerin) into mass. By using the density of nitroglycerin, we can find the total mass of the sample, which is necessary for calculating the number of moles of nitroglycerin present before applying stoichiometry.

Gas Laws

Gas laws describe the behavior of gases under various conditions of temperature and pressure. In this context, the ideal gas law (PV=nRT) can be applied to relate the number of moles of gas produced to the volume and pressure of the gases generated from the detonation of nitroglycerin. Understanding these principles helps in predicting the behavior of the gaseous products formed during the reaction.

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