Question

How many total moles of ions are released when each of the following dissolves in water? (a) \(0.734 \mathrm{~mol}\) of \(\mathrm{Na}_{2} \mathrm{HPO}_{4}\) (b) \(3.86 \mathrm{~g}\) of \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) (c) \(8.66 \times 10^{20}\) formula units of \(\mathrm{NiCl}_{2}\)

Short answer

Total moles of ions: (a) 2.20 mol, (b) 0.0310 mol, (c) 4.32 \times 10^{-3} mol.

Step-by-step solution

Identify the ions and their quantities

For each compound, determine the ions formed upon dissolution and their respective quantities in one formula unit.(a) \(\text{Na}_{2} \text{HPO}_{4}\) dissociates into 2 Na\( ^{+}\) and 1 HPO\( _{4}^{2-}\).(b) \(\text{CuSO}_{4} \cdot 5 \text{H}_{2} \text{O}\) dissociates into Cu\( ^{2+}\) and SO\( _{4}^{2-}\), with the water providing no additional ions.(c) NiCl\( _{2}\) dissociates into Ni\( ^{2+}\) and 2 Cl\( ^{-}\).

Calculate the total moles of ions for Na2HPO4

Given 0.734 mol of \(\text{Na}_{2} \text{HPO}_{4}\), calculate the total moles of ions:Each formula unit of \(\text{Na}_{2} \text{HPO}_{4}\) produces 3 moles of ions (2 Na\( ^{+}\) and 1 HPO\( _{4}^{2-}\)).Total moles of ions = 0.734 mol \times 3 = 2.202 mol.

Calculate the moles of CuSO4·5H2O

First, find the molar mass of \(\text{CuSO}_{4} \cdot 5\text{H}_{2}\text{O}\):- Cu = 63.55 g/mol- S = 32.07 g/mol- O = 4 \times 16.00 g/mol = 64.00 g/mol- 5 H\( _{2}\)O = 5 \times (2 \times 1.01 + 16.00) g/mol = 90.10 g/molMolar mass = 63.55 + 32.07 + 64.00 + 90.10 = 249.72 g/molGiven 3.86 g of \(\text{CuSO}_{4} \cdot 5\text{H}_{2}\text{O}\), calculate the moles:Moles = 3.86 g / 249.72 g/mol ≈ 0.0155 mol.Each formula unit of \(\text{CuSO}_{4}\) provides 2 moles of ions.Total moles of ions = 0.0155 mol \times 2 = 0.0310 mol.

Calculate the moles of NiCl2 using Avogadro's number

Given 8.66 \times 10^{20} formula units of \(\text{NiCl}_{2}\), convert to moles using Avogadro's number (6.022 \times 10^{23} units/mol).Moles of \(\text{NiCl}_{2}\) = \frac{8.66 \times 10^{20}}{6.022 \times 10^{23}} ≈ 1.44 \times 10^{-3} mol.Each formula unit of \(\text{NiCl}_{2}\) produces 3 moles of ions (1 Ni\( ^{2+}\) and 2 Cl\( ^{-}\)).Total moles of ions = 1.44 \times 10^{-3} mol \times 3 = 4.32 \times 10^{-3} mol.

Key concepts

Mole Calculations

When solving chemistry problems, you need to perform mole calculations frequently. A 'mole' is a unit in chemistry that represents a specific quantity of particles, such as atoms, molecules, or ions.
Mole calculations involve converting between grams, moles, and the number of particles.
For instance, when given the mass of a substance, you can calculate the number of moles by dividing the mass by its molar mass (i.e., grams per mole).
Conversely, to find the mass of a substance if given the number of moles, just multiply the number of moles by the molar mass.
This is crucial for understanding how much of a substance reacts or gets produced in a chemical reaction.

Ions in Solution

When ionic compounds dissolve in water, they break apart into ions. This process is called dissociation.
The number of moles of ions released depends on the chemical formula of the compound.
For example, Na2HPO4 dissociates into 2 Na+ ions and 1 HPO4^2- ion, giving a total of 3 ions.
To find the total moles of ions produced, you multiply the moles of the compound by the number of ions per formula unit.
So for 0.734 moles of Na2HPO4, it would be 0.734 moles * 3 ions/mole = 2.202 moles of ions.
Understanding this concept is key to predicting the behavior of ionic solutions.

Avogadro's Number

Avogadro's number (6.022 x 10^23) is a fundamental constant in chemistry.
It's the number of atoms, molecules, or ions in one mole of a substance.
For example, if you have 8.66 x 10^20 formula units of NiCl2, you can convert this to moles by dividing by Avogadro's number: (8.66 x 10^20) / (6.022 x 10^23) ≈ 1.44 x 10^-3 moles.
Understanding Avogadro's number allows you to move between large quantities of atoms or molecules and practical laboratory-sized amounts.
It's essential for calculations involving particles in a given amount of substance.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, measured in grams per mole (g/mol).
It's calculated by adding the atomic masses of all the atoms in a molecule.
For example, for CuSO4·5H2O:

• Cu = 63.55 g/mol
• S = 32.07 g/mol
• O = 16.00 g/mol (four of them, so 4*16.00 = 64.00 g/mol)
• 5H2O = 5*(2*1.01 + 16.00) = 90.10 g/mol

Adding these: 63.55 + 32.07 + 64.00 + 90.10 = 249.72 g/mol.
This helps you convert between mass and moles in chemical reactions.
It’s a foundational concept in stoichiometry, which allows you to predict products and reactants in given chemical reactions.