Ammonium nitrate, a potential ingredient of terrorist bombs, can be made nonexplosive by addition of diammo-nium hydrogen phosphate, (NH4)2HPO4. Analysis of such a NH4NO3 - (NH4)2HPO4 mixture showed the mass percent of nitrogen to be 30.43%. What is the mass ratio of the two components in the mixture?

Verified step by step guidance

1. Determine the molar mass of ammonium nitrate (NH4NO3) and diammonium hydrogen phosphate ((NH4)2HPO4).
2. Calculate the mass percent of nitrogen in pure ammonium nitrate and in pure diammonium hydrogen phosphate using their chemical formulas.
3. Let x be the mass of ammonium nitrate and y be the mass of diammonium hydrogen phosphate in the mixture. Set up the equation for the total mass of the mixture as x + y.
4. Set up an equation based on the given mass percent of nitrogen in the mixture (30.43%). Use the mass percent nitrogen in each compound and their respective masses (x and y) to express the total mass of nitrogen in the mixture.
5. Solve the system of equations from steps 3 and 4 to find the ratio x/y, which represents the mass ratio of ammonium nitrate to diammonium hydrogen phosphate in the mixture.

Key Concepts

Mass Percent Composition

Mass percent composition is a way to express the concentration of a component in a mixture. It is calculated by taking the mass of the component divided by the total mass of the mixture, then multiplying by 100. In this question, the mass percent of nitrogen in the mixture is given, which is crucial for determining the mass ratio of the two components.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on the conservation of mass. It allows us to relate the amounts of different substances in a mixture. In this case, understanding the stoichiometric relationships between ammonium nitrate and diammonium hydrogen phosphate will help in determining their mass ratio based on the nitrogen content.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is essential for converting between mass and moles in chemical calculations. To find the mass ratio of the components in the mixture, the molar masses of ammonium nitrate and diammonium hydrogen phosphate must be calculated to relate their masses to the nitrogen content.