Question

Ammonium nitrate has been used as a high explosive because it is unstable and decomposes into several gaseous substances. The rapid expansion of the gaseous substances produces the explosive force. $$\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \rightarrow \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$$ Calculate the mass of each product gas if \(1.25 \mathrm{g}\) of ammonium nitrate reacts.

Short answer

When 1.25g of ammonium nitrate reacts, the mass of each gaseous product formed is: \(N_2: 0.4363g\), \(O_2: 0.4992g\), and \(H_2O: 0.2811g\).

Step-by-step solution

Calculate the molar mass of ammonium nitrate and all products

We need to find the molar masses of the reactant (NH₄NO₃) and products (N₂, O₂, and H₂O) to convert mass to moles and vice versa. NH₄NO₃: (1 x 14.01) + (4 x 1.01) + (1 x 14.01) + (3 x 16) = 80.05 g/mol N₂: 2 x 14.01 = 28.02 g/mol O₂: 2 x 16 = 32 g/mol H₂O: (2 x 1.01) + 16 = 18.02 g/mol

Calculate the moles of ammonium nitrate

To find the moles of ammonium nitrate, we will use the given mass (1.25 g) and divide it by the molar mass (80.05 g/mol) calculated in Step 1. Moles of NH₄NO₃ = (1.25 g) / (80.05 g/mol) = 0.0156 mol

Use stoichiometry to find the moles of each product

The stoichiometry of the balanced chemical equation shows a 1:1 ratio between the reactants and each product. Therefore, the moles of each product are equal to the moles of the reactant. Moles of N₂ = 0.0156 mol Moles of O₂ = 0.0156 mol Moles of H₂O = 0.0156 mol

Calculate the mass of each product

Using the moles of each product and their respective molar masses obtained in Step 1, we can now calculate the mass of each gaseous product. Mass of N₂ = (0.0156 mol) x (28.02 g/mol) = 0.4363 g Mass of O₂ = (0.0156 mol) x (32 g/mol) = 0.4992 g Mass of H₂O = (0.0156 mol) x (18.02 g/mol) = 0.2811 g Thus, the mass of each gaseous product formed when 1.25g of ammonium nitrate reacts is: - N₂: 0.4363 g - O₂: 0.4992 g - H₂O: 0.2811 g

Key concepts

Molar Mass Calculation

Molar mass is a fundamental concept in chemistry that relates to the mass of one mole of a substance. It allows you to convert between the mass of a compound and the number of moles, which represents the number of molecules or atoms present.

• The molar mass of a compound is determined by summing up the atomic masses of its constituent elements, based on their presence in the chemical formula.
• For instance, in ammonium nitrate (NH₄NO₃), the molar mass is calculated by adding the atomic masses of nitrogen, hydrogen, and oxygen in the compound:
  • Nitrogen contributes two atoms each with an atomic mass of 14.01,
  • Hydrogen contributes four atoms each with an atomic mass of 1.01,
  • Oxygen contributes three atoms each with an atomic mass of 16.
  So, the total molar mass = (1 x 14.01) + (4 x 1.01) + (1 x 14.01) + (3 x 16) = 80.05 g/mol.
• This calculation is essential as it lays the groundwork for converting the mass of the compound into moles, a process necessary for stoichiometric calculations.

Stoichiometry

Stoichiometry involves understanding and using the quantitative relationships in chemical reactions. In essence, it helps you predict the amounts of substances consumed or produced.

• To determine this, one must first write a balanced chemical equation, which ensures mass conservation of each element.
• A crucial aspect is the mole ratio, which is derived from the coefficients of the substances in the balanced equation. In the decomposition of ammonium nitrate to produce N₂, O₂, and H₂O, there's a stoichiometric ratio of 1:1, indicating that one mole of NH₄NO₃ yields one mole of each product.
• This concept allows you to determine how the amount of reactant relates to the amount of products. For instance, if you know the moles of NH₄NO₃, you directly know the moles of each product as they have a 1:1 relationship.

Chemical Reaction Decomposition

Chemical decomposition is a type of chemical reaction where one compound breaks down into two or more simpler substances. Ammonium nitrate, for example, decomposes to form nitrogen, oxygen, and water vapor.

• Decomposition reactions often require energy, like heat, to break chemical bonds in the compound. In the case of ammonium nitrate, this results in gaseous products that expand rapidly, demonstrating explosive characteristics.
• Such a reaction can be represented by a simple equation: NH₄NO₃(s) → N₂(g) + O₂(g) + H₂O(g). This explains the transformation of a solid reactant into gaseous products, illustrating conservation of mass where the mass of reactants equals the mass of products in terms of both quantity and type of atoms.
• This particular decomposition is important industrially and historically due to its explosive potential, highlighting the significance of understanding chemical processes both in educational settings and practical applications.