Question

. Acetone peroxide, C9H18O6(s), is a powerful but highly unstable explosive that does not contain nitrogen. It can pass undetected through scanners designed to detect the presence of nitrogen in explosives like TNT (trinitrotoluene, C7H5N3O6), or ammonium nitrate. (a) Write a balanced equation for the combustion (burning in oxygen) of acetone peroxide producing steam and carbon dioxide. (b) What pressure is generated in a 2.00-L bottle when 5.00 g of acetone peroxide is ignited to 5558C and burned in air? Assume 100% combustion.

Short answer

Answer: The pressure generated in the 2.00-L bottle is approximately 823.47 atm.

Step-by-step solution

(a) Write the balanced combustion equation for acetone peroxide

The products of the combustion of acetone peroxide (C9H18O6) are water (H2O) and carbon dioxide (CO2). The unbalanced equation is: C9H18O6 + O2 -> H2O + CO2 Now balance the equation by adjusting the coefficients: C9H18O6 + 9O2 -> 9H2O + 9CO2 So, the balanced equation is: C9H18O6(s) + 9O2(g) -> 9H2O(g) + 9CO2(g)

(b) Calculate the pressure generated by burning 5.00g of acetone peroxide

We'll use the ideal gas law (PV=nRT) for this calculation. First, let's find the number of moles (n). Molar mass of acetone peroxide (C9H18O6) = (9×12.01) + (18×1.01) + (6×16.00) = 222.27 g/mol 5.00g of acetone peroxide = 5.00g / 222.27g/mol = 0.0225 mol Now, we need to find the number of moles of products produced from the balanced equation in part (a). For every 1 mol of acetone peroxide, 9 moles of water vapor and 9 moles of carbon dioxide are produced: 0.0225 mol of acetone peroxide produces (9×0.0225) + (9×0.0225) = 0.405 mol The given temperature is 5558℃. Convert it to Kelvin: Temperature (T) = (5558 + 273.15) = 5831.15 K Now we can apply the ideal gas law (PV=nRT) using the number of moles of products (n=0.405), given volume (V=2.00L), temperature (T=5831.15K), and ideal gas constant (R=0.0821 L·atm/mol·K): P × 2.00 = 0.405 × 0.0821 × 5831.15 P = (0.405 × 0.0821 × 5831.15) / 2.00 P ≈ 823.47 atm The pressure generated in the 2.00-L bottle is approximately 823.47 atm.

Key concepts

Chemical Reactions

Understanding the nature of chemical reactions is essential for students studying chemistry. A chemical reaction involves the transformation of one or more substances, known as reactants, into different substances, called products. The combustion reaction is a prime example where a substance combines with oxygen to release energy in the form of heat or light. In the case of acetone peroxide, the reaction is particularly vigorous, producing carbon dioxide and water vapor as the byproducts.

This type of reaction is exothermic, meaning it releases energy, which is why substances like acetone peroxide are used as explosives. The ability to write and balance chemical equations is a fundamental skill for understanding such reactions. This involves ensuring that the same number of atoms for each element is present on both sides of the reaction equation, thereby adhering to the Law of Conservation of Mass.

Ideal Gas Law

The ideal gas law is a crucial equation in chemistry and physics that describes the behavior of an ideal gas. It is given by the formula
\(PV = nRT\)
where P represents pressure, V stands for volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvins. Calculating the pressure produced by a chemical reaction, like the combustion of acetone peroxide, relies on understanding this law.

In the problem, we compute the pressure inside a container after the explosive is ignited. We account for the change in state from solid to gas and use the Ideal Gas Law to quantify the pressure resulting from the reaction. Doing so is critical not only in theoretical chemistry but also in practical applications, such as engineering and safety protocols for handling materials that undergo rapid decomposition or combustion.

Balancing Chemical Equations

Balancing chemical equations is not just a mathematical exercise; it's a reflection of matter conservation during a chemical reaction. Each element must have the same number of atoms before and after the reaction, respecting the fundamental principle that matter cannot be created or destroyed.

When balancing the combustion reaction for acetone peroxide, we look at the subscripts of atoms in the chemical formula and adjust the coefficients in front of each compound accordingly. This ensures that every atom on the reactant side is accounted for on the product side. For acetone peroxide, multiple moles of oxygen gas react to produce several moles of water and carbon dioxide.

Mastery of balancing equations leads to a deeper comprehension of reaction stoichiometry, which is essential for predicting the outcome of reactions, as seen in calculating the pressure in the aforementioned exercise.