Question

How many moles of ions are in each compound? a. 0.0200 g of AgNO \(_{3}\) b. 0.100 mol of \(\mathrm{K}_{2} \mathrm{CrO}_{4}\) c. 0.500 \(\mathrm{g}\) of \(\mathrm{Ba}(\mathrm{OH})_{2}\) d. \(1.00 \times 10^{-9} \mathrm{mol}\) of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\)

Short answer

a. \(2.36 \times 10^{-4}\) mol of ions in 0.0200 g of AgNO3 b. 0.300 mol of ions in 0.100 mol of K2CrO4 c. \(8.76 \times 10^{-3}\) mol of ions in 0.500 g of Ba(OH)2 d. \(3.00 \times 10^{-9}\) mol of ions in \(1.00 \times 10^{-9}\) mol of Na2CO3

Step-by-step solution

Find the dissociation of each compound

First, we must examine the dissociation of each compound into ions in a solution: a. AgNO3 → Ag+ + NO3- b. K2CrO4 → 2 K+ + CrO42- c. Ba(OH)2 → Ba2+ + 2 OH- d. Na2CO3 → 2 Na+ + CO32-

Calculate moles of ions for each compound

Now that we know the stoichiometry of ions produced by each compound, we can calculate the moles of each ion based on the given moles or grams of the compounds. a. AgNO3: We have 0.0200 g of AgNO3. First, find the molar mass of AgNO3: 107.87 + 14.01 + (3 × 16.00) = 169.87 g/mol Now, convert grams of AgNO3 to moles: (0.0200 g)/(169.87 g/mol) = 1.18 × 10^-4 mol Since 1 mol of AgNO3 produces 1 Ag+ ion and 1 NO3- ion, the total moles of ions will be twice the moles of AgNO3: 2 × (1.18 × 10^-4 mol) = 2.36 × 10^-4 mol b. K2CrO4: We already have the moles of K2CrO4, which is 0.100 mol. Since 1 mol of K2CrO4 produces 2 K+ ions and 1 CrO42- ion, the total moles of ions will be three times the moles of K2CrO4: 3 × (0.100 mol) = 0.300 mol c. Ba(OH)2: We have 0.500 g of Ba(OH)2. First, find the molar mass of Ba(OH)2: 137.3 + 2(15.999) + 2(1.008) = 171.342 g/mol Now, convert grams of Ba(OH)2 to moles: (0.500 g)/(171.342 g/mol) = 2.92 × 10^-3 mol Since 1 mol of Ba(OH)2 produces 1 Ba2+ ion and 2 OH- ions, the total moles of ions will be three times the moles of Ba(OH)2: 3 × (2.92 × 10^-3 mol) = 8.76 × 10^-3 mol d. Na2CO3: We already have the moles of Na2CO3, which is 1.00 × 10^-9 mol. Since 1 mol of Na2CO3 produces 2 Na+ ions and 1 CO32- ion, the total moles of ions will be three times the moles of Na2CO3: 3 × (1.00 × 10^-9 mol)= 3.00 × 10^-9 mol

Provide answers

Now we can write the answers for the number of moles of ions in each compound: a. 2.36 × 10^-4 mol of ions in 0.0200 g of AgNO3 b. 0.300 mol of ions in 0.100 mol of K2CrO4 c. 8.76 × 10^-3 mol of ions in 0.500 g of Ba(OH)2 d. 3.00 × 10^-9 mol of ions in 1.00 × 10^-9 mol of Na2CO3

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves the calculation of reactants and products in chemical reactions. It is based on the law of conservation of mass, which states that in any chemical reaction, matter is neither created nor destroyed. Therefore, the amount of each element must be the same in the reactants and products.

Understanding stoichiometry requires a firm grasp of the mole concept, which allows chemists to count atoms, molecules, and ions in terms of a common unit—the mole. A mole is equivalent to Avogadro's number (\(6.022 \times 10^{23}\)) of particles.

Ionic Compound Dissociation and Stoichiometry

In the context of ionic compounds, stoichiometry is used to determine the quantity of ions produced when a compound dissociates in solution. For example, the dissociation of AgNO₃ yields an equal number of Ag⁺ and NO₃⁻ ions. Thus, stoichiometry can be applied to calculate the total moles of ions formed from a given amount of an ionic compound.

Molar Mass Calculation

The molar mass of a substance is the mass of one mole of its particles and is expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms in the formula of the substance. The atomic masses are found on the periodic table and typically have units of atomic mass unit (amu) or grams per mole (g/mol).

To calculate the molar mass of AgNO₃, for instance, one would add the molar masses of one silver (Ag) atom, one nitrogen (N) atom, and three oxygen (O) atoms together. This sum gives the total molar mass of the compound, which is essential in converting between grams of a substance and moles, thereby linking stoichiometry with quantitative measurements in the laboratory.

Applying Molar Mass in Stoichiometry

The molar mass is a critical conversion factor in stoichiometry, enabling the translation of a compound's mass into the amount in moles, and subsequently, the calculation of moles of ions generated upon dissociation, providing a bridge between the mass of a substance and its mole quantity.

Dissociation of Ionic Compounds

Ionic compounds are composed of positively charged ions (cations) and negatively charged ions (anions) held together by electrostatic forces in a lattice structure. When dissolved in water, these compounds dissociate into their constituent ions, a process essential for many biochemical reactions and industrial processes.

To predict the number of moles of ions resulting from dissociation, one must understand the formula of the original compound. For example, Ba(OH)₂ dissociates into one Ba²⁺ ion and two OH⁻ ions. Accordingly, the dissociation equation provides information about the stoichiometry of the dissociation.

The Role of Dissociation in Solution Stoichiometry

The dissociation of ionic compounds into their ions in solution impacts various stoichiometric calculations. For example, calculating the concentration of ions in a solution requires knowledge of both the stoichiometry of dissolving—how many of each ion type are produced—and the amount of the compound that has been dissolved. This understanding is vital for tasks like analyzing the purity of water or the effectiveness of a chemical reaction.