Question

For each of the following samples of ionic substances, calculate the number of moles and mass of the positive ions present in each sample. a. \(4.25 \mathrm{~g}\) of ammonium iodide, \(\mathrm{NH}_{4} \mathrm{I}\) b. 6.31 moles of ammonium sulfide, \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{~S}\) c. \(9.71 \mathrm{~g}\) of barium phosphide, \(\mathrm{Ba}_{3} \mathrm{P}_{2}\) d. 7.63 moles of calcium phosphate, \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)

Short answer

a) In 4.25 g of ammonium iodide, there are 0.0293 moles of NH4+ ions with a mass of 0.529 g. b) In 6.31 moles of ammonium sulfide, there are 12.62 moles of NH4+ ions with a mass of 227.79 g. c) In 9.71 g of barium phosphide, there are 0.0615 moles of Ba2+ ions with a mass of 8.44 g. d) In 7.63 moles of calcium phosphate, there are 22.89 moles of Ca2+ ions with a mass of 917.84 g.

Step-by-step solution

a. 4.25 g of ammonium iodide (NH4I)

First, we need to calculate the number of moles of NH4I. To do this, we'll find the molar mass of NH4I and then divide the given mass (4.25 g) by the molar mass. Molar mass of NH4I = 1(14.01 + 1.01*4) + 1(126.9) = 68.05 + 126.9 = 144.95 g/mol Number of moles of NH4I = (4.25 g) / (144.95 g/mol) = 0.0293 mol Next, we need to find the number of moles of NH4+ ions in the sample. In one mole of NH4I, there is one mole of NH4+ ion. Therefore: Number of moles of NH4+ ions = 0.0293 mol Now, we need to find the mass of NH4+ ions in the sample. For this, we'll use the molar mass of NH4+ ion and multiply it by the number of moles. Molar mass of NH4+ ion = 14.01 + 1.01*4 = 18.05 g/mol Mass of NH4+ ions = (0.0293 mol) * (18.05 g/mol) = 0.529 g

b. 6.31 moles of ammonium sulfide ((NH4)2S)

We are given the number of moles of (NH4)2S, so there is no need to calculate it in this case. Number of moles of (NH4)2S = 6.31 mol Next, we need to find the number of moles of NH4+ ions in the sample. In one mole of (NH4)2S, there are two moles of NH4+ ions. Therefore: Number of moles of NH4+ ions = 6.31 mol * 2 = 12.62 mol Now, we need to find the mass of NH4+ ions in the sample. We'll use the molar mass of NH4+ ion, which we found earlier. Mass of NH4+ ions = (12.62 mol) * (18.05 g/mol) = 227.79 g

c. 9.71 g of barium phosphide (Ba3P2)

First, we need to calculate the number of moles of Ba3P2. To do this, we'll find the molar mass of Ba3P2 and then divide the given mass (9.71 g) by the molar mass. Molar mass of Ba3P2 = 3(137.3) + 2(30.97) = 411.9 + 61.94 = 473.84 g/mol Number of moles of Ba3P2 = (9.71 g) / (473.84 g/mol) = 0.0205 mol Next, we need to find the number of moles of Ba2+ ions in the sample. In one mole of Ba3P2, there are three moles of Ba2+ ions. Therefore: Number of moles of Ba2+ ions = 0.0205 mol * 3 = 0.0615 mol Now, we need to find the mass of Ba2+ ions in the sample. For this, we'll use the molar mass of Ba2+ ion. Molar mass of Ba2+ ion = 137.3 g/mol Mass of Ba2+ ions = (0.0615 mol) * (137.3 g/mol) = 8.44 g

d. 7.63 moles of calcium phosphate (Ca3(PO4)2)

We are given the number of moles of Ca3(PO4)2, so there is no need to calculate it in this case. Number of moles of Ca3(PO4)2 = 7.63 mol Next, we need to find the number of moles of Ca2+ ions in the sample. In one mole of Ca3(PO4)2, there are three moles of Ca2+ ions. Therefore: Number of moles of Ca2+ ions = 7.63 mol * 3 = 22.89 mol Now, we need to find the mass of Ca2+ ions in the sample. For this, we'll use the molar mass of Ca2+ ion. Molar mass of Ca2+ ion = 40.08 g/mol Mass of Ca2+ ions = (22.89 mol) * (40.08 g/mol) = 917.84 g

Key concepts

Molar Mass

Understanding the concept of molar mass is fundamental in chemistry, especially when dealing with reactions and compounds. In essence, the molar mass of a substance is the mass in grams of one mole of that substance. It is a bridge between the mass of a material and the amount of substance (measured in moles) we have.

For instance, the molar mass of an ammonium ion (NH₄⁺) is calculated by adding together the atomic masses of nitrogen (14.01 g/mol) and four hydrogen atoms (4 × 1.01 g/mol), yielding a molar mass of 18.05 g/mol. This molar mass helps us determine how much one mole of NH₄⁺ ions weighs, which is crucial when converting between mass and moles in stoichiometry problems.

When calculating molar mass for ionic compounds, such as barium phosphide (Ba₃P₂), we sum the molar masses of all the constituent atoms within one formula unit of the compound. Each barium atom contributes 137.3 g/mol and each phosphorus atom contributes 30.97 g/mol. Thus, we multiply these by their respective quantity in the formula and add them together to find the total molar mass of the compound.

Stoichiometry

Stoichiometry is the section of chemistry that pertains to the quantitative aspects of chemical reactions. This topic provides us with the tools to predict the amounts of reactants and products involved in a chemical reaction. An essential aspect of this is understanding the relationship between moles of different compounds in a reaction.

Consider the stoichiometry of ammonium sulfide ((NH₄)₂S), where we determine the moles of positive ions (NH₄⁺) present. Knowing that each formula unit of ammonium sulfide contains two ammonium ions, we can conclude that for every mole of (NH₄)₂S, we will have two moles of NH₄⁺. This step, multiplying the moles of the compound by the number of ammonium ions per formula unit, shows the power of stoichiometric relationships.

Furthermore, stoichiometry can tell us about the conservation of mass in a reaction. By ensuring that the sum of the mass of reactants equals the sum of the mass of products, stoichiometry reinforces the idea that in a chemical reaction, matter is neither created nor destroyed but simply rearranged.

Ionic Compounds

Ionic compounds, such as calcium phosphate (Ca₃(PO₄)₂), are formed from the electrostatic attraction between ions, which are atoms or groups of atoms that have gained or lost electrons and thus carry a charge. Positive ions (cations) and negative ions (anions) come together to form a neutral compound.

Ionic compounds usually form crystalline structures and have high melting and boiling points due to the strong ionic bonds between the ions. In the context of moles and mass calculations, ionic compounds often require us to focus on a particular ion within the compound. For example, when asked to find the mass of positive ions in calcium phosphate, we focus solely on the calcium ions (Ca²⁺).

Since each formula unit of calcium phosphate contains three calcium ions, we can use this stoichiometric ratio to determine the number of moles of calcium ions based on the moles of calcium phosphate. This direct relationship between the stoichiometry of the compound and its constituent ions is key to successfully solving many chemical problems involving ionic compounds.