Question

What is the molarity of each ion present in aqueous solutions prepared by dissolving \(20.00 \mathrm{~g}\) of the following compounds in water to make 4.50 L of solution? (a) cobalt(III) chloride (b) nickel(III) sulfate (c) sodium permanganate (d) iron(II) bromide

Short answer

Question: Calculate the molarity of each ion present in the solutions after dissolving the following compounds in 4.50 L of water: (a) 20.00 g of cobalt(III) chloride, (b) 20.00 g of nickel(III) sulfate, (c) 20.00 g of sodium permanganate, and (d) 20.00 g of iron(II) bromide. Answer: The molarity of each ion present in the solutions is as follows: (a) Co³⁺: 0.0269 M, Cl⁻: 0.0807 M (b) Ni³⁺: 0.0219 M, SO₄²⁻: 0.0329 M (c) Na⁺: 0.0313 M, MnO₄⁻: 0.0313 M (d) Fe²⁺: 0.0206 M, Br⁻: 0.0412 M

Step-by-step solution

(a) Determine the formula of cobalt(III) chloride

Cobalt(III) chloride has a cobalt ion with a +3 charge: Co³⁺ and a chloride ion with a -1 charge: Cl⁻. To balance the charges, we need 3 chloride ions for each cobalt ion. Thus, the formula for cobalt(III) chloride is CoCl₃.

(a) Calculate the molar mass of CoCl₃

The molar mass of CoCl₃ can be calculated by adding the individual molar masses of cobalt and chloride. The molar mass of cobalt (Co) is 58.93 g/mol, and the molar mass of chloride (Cl) is 35.45 g/mol. Hence, the molar mass of CoCl₃ is: Molar mass = \(58.93 + (3 \times 35.45) = 58.93 + 106.35 = 165.28 \mathrm{~g/mol}\)

(a) Find the moles of CoCl₃

Given the mass of CoCl₃ as 20.00 g, we can find the moles of CoCl₃ using the following formula: Moles = Mass / Molar mass Moles = \(20.00 / 165.28 = 0.121 \mathrm{~mol}\)

(a) Calculate the molarity of each ion present

We have a 0.121 mol of CoCl₃ dissolved in 4.50 L of the solution. This means: Molarity of Co³⁺ = moles of Co³⁺ / volume of solution = \(0.121 / 4.50 = 0.0269 \mathrm{~M}\) Since there are 3 moles of Cl⁻ for every mole of Co³⁺, the moles of Cl⁻ = \(3 \times 0.121 = 0.363 \mathrm{~mol}\). Molarity of Cl⁻ = moles of Cl⁻ / volume of solution = \(0.363 / 4.50 = 0.0807 \mathrm{~M}\)

(b) Determine the formula of nickel(III) sulfate

Nickel(III) sulfate has a nickel ion with a +3 charge: Ni³⁺ and a sulfate ion with a -2 charge: SO₄²⁻. To balance the charges, we need 2 nickel ions and 3 sulfate ions. Thus, the formula for nickel(III) sulfate is Ni₂(SO₄)₃.

(b) Calculate the molar mass of Ni₂(SO₄)₃

The molar mass of Ni₂(SO₄)₃ can be calculated by adding the individual molar masses of nickel and sulfate. The molar mass of nickel (Ni) is 58.69 g/mol, and the molar mass of sulfate (SO₄) is 96.06 g/mol. So, the molar mass of Ni₂(SO₄)₃ is: Molar mass = \((2 \times 58.69) + (3 \times 96.06) = 117.38 + 288.18 = 405.56 \mathrm{~g/mol}\)

(b) Find the moles of Ni₂(SO₄)₃

Given the mass of Ni₂(SO₄)₃ as 20.00 g, we can find the moles of Ni₂(SO₄)₃ using the following formula: Moles = Mass / Molar mass Moles = \(20.00 / 405.56 = 0.0493 \mathrm{~mol}\)

(b) Calculate the molarity of each ion present

We have 0.0493 mol of Ni₂(SO₄)₃ dissolved in 4.50 L of the solution: Molarity of Ni³⁺ = (2 × moles of Ni³⁺) / volume of solution = \((2 \times 0.0493) / 4.50 = 0.0219 \mathrm{~M}\) Since there are 3 moles of SO₄²⁻ for every mole of Ni₂(SO₄)₃, the moles of SO₄²⁻ = \(3 \times 0.0493 = 0.1479 \mathrm{~mol}\). Molarity of SO₄²⁻ = moles of SO₄²⁻ / volume of solution = \(0.1479 / 4.50 = 0.0329 \mathrm{~M}\)

(c) Determine the formula of sodium permanganate

Sodium permanganate has a sodium ion with a +1 charge: Na⁺ and a permanganate ion with a -1 charge: MnO₄⁻. The charges are already balanced, so the formula for sodium permanganate is NaMnO₄.

(c) Calculate the molar mass of NaMnO₄

The molar mass of NaMnO₄ can be calculated by adding the individual molar masses of sodium, manganese, and oxygen. The molar mass of sodium (Na) is 22.99 g/mol, the molar mass of manganese (Mn) is 54.94 g/mol, and the molar mass of oxygen (O) is 16.00 g/mol. The molar mass of NaMnO₄ is: Molar mass = \(22.99 + 54.94 + (4 \times 16.00) = 22.99 + 54.94 + 64.00 = 141.93 \mathrm{~g/mol}\)

(c) Find the moles of NaMnO₄

Given the mass of NaMnO₄ as 20.00 g, we can find the moles of NaMnO₄ using the following formula: Moles = Mass / Molar mass Moles = \(20.00 / 141.93 = 0.141 \mathrm{~mol}\)

(c) Calculate the molarity of each ion present

We have 0.141 mol of NaMnO₄ dissolved in 4.50 L of the solution. Molarity of Na⁺ = moles of Na⁺ / volume of solution = \(0.141 / 4.50 = 0.0313 \mathrm{~M}\) Molarity of MnO₄⁻ = moles of MnO₄⁻ / volume of solution = \(0.141 / 4.50 = 0.0313 \mathrm{~M}\)

(d) Determine the formula of iron(II) bromide

Iron(II) bromide has an iron ion with a +2 charge: Fe²⁺ and a bromine ion with a -1 charge: Br⁻. To balance the charges, we need 2 bromine ions for each iron ion. Thus, the formula for iron(II) bromide is FeBr₂.

(d) Calculate the molar mass of FeBr₂

The molar mass of FeBr₂ can be calculated by adding the individual molar masses of iron and bromine. The molar mass of iron (Fe) is 55.85 g/mol, and the molar mass of bromine (Br) is 79.90 g/mol. The molar mass of FeBr₂ is: Molar mass = \(55.85 + (2 \times 79.90) = 55.85 + 159.80 = 215.65 \mathrm{~g/mol}\)

(d) Find the moles of FeBr₂

Given the mass of FeBr₂ as 20.00 g, we can find the moles of FeBr₂ using the following formula: Moles = Mass / Molar mass Moles = \(20.00 / 215.65 = 0.0927 \mathrm{~mol}\)

(d) Calculate the molarity of each ion present

We have 0.0927 mol of FeBr₂ dissolved in 4.50 L of the solution. Molarity of Fe²⁺ = moles of Fe²⁺ / volume of solution = \(0.0927 / 4.50 = 0.0206 \mathrm{~M}\) Since there are 2 moles of Br⁻ for every mole of Fe²⁺, the moles of Br⁻ = \(2 \times 0.0927 = 0.1854 \mathrm{~mol}\). Molarity of Br⁻ = moles of Br⁻ / volume of solution = \(0.1854 / 4.50 = 0.0412 \mathrm{~M}\)

Key concepts

Ionic Compounds

Ionic compounds are formed when elements combine due to opposite electrical charges. A typical ionic bond involves a metal that donates one or more electrons to a non-metal, resulting in positively charged metal cations and negatively charged non-metal anions. For instance, in cobalt(III) chloride, cobalt ions with a +3 charge pair with three chloride ions, each having a -1 charge, to ensure electrical neutrality in the chemical formula CoCl₃.
Nickel(III) sulfate highlights a slightly different composition with two nickel ions of +3 charge each combining with three sulfate ions, creating the compound Ni₂(SO₄)₃ where the overall charge balance is maintained.
Likewise, sodium permanganate, being NaMnO₄, pairs the +1 sodium ion with a -1 permanganate ion, exhibiting the simplicity of a one-to-one charge balance. Lastly, in iron(II) bromide (FeBr₂), an iron ion with a +2 charge bonds with two bromide ions of -1 charge each, keeping the compound electrically neutral.
Understanding these charge interactions is crucial when calculating the molarity of ions in solutions.

Molar Mass Calculation

Calculating molar mass is a fundamental skill in chemistry when working with ionic compounds. The molar mass signifies the mass of a given substance (in grams) as one mole, which is equivalent to the substance's formula weight expressed in atomic mass units. Let's break this process down:
You derive the molar mass by summing the atomic masses of all atoms in a molecule. For example, cobalt(III) chloride's molar mass combines the atomic mass of one cobalt atom (58.93 g/mol) and three chloride atoms (3 x 35.45 g/mol), culminating in 165.28 g/mol.
For nickel(III) sulfate, compute with the molar mass of two nickel atoms (58.69 g/mol each) and three sulfate groups (96.06 g/mol each), leading to a total of 405.56 g/mol. This sum provides the mass of one mole of the compound. Such calculations are essential for determining how many molecules are present in any given mass of the compound, facilitating the subsequent calculations of mole-based concentrations and reactions in aqueous solutions.

Aqueous Solutions

Aqueous solutions are mixtures wherein water acts as the solvent. In chemistry, many reactions and compounds are studied within these solutions due to water's exceptional capacity to dissolve numerous substances. Upon dissolving ionic compounds in water, they dissociate into their respective ions.
When the compound cobalt(III) chloride, for instance, dissolves, it forms distinct cobalt and chloride ions evenly dispersed throughout the liquid. The molarity of each ion in such a solution depends on both the number of moles of the dissolved compound and the volume of the solution at hand.
Molarity is calculated using the formula \( M = \frac{n}{V} \), where \(n\) is the number of moles of solute, and \(V\) is the volume of the solution in liters. It's in the aqueous framework that we measure ion concentrations to predict reactions and behaviors in different chemical environments. Recognizing the unique dynamics of aqueous solutions allows chemists to tailor their approaches when working with a range of chemical reactions.