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Chapter 4: Problem 21

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

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

Step by step solution

01

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\( ^{-}\).
02

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.
03

Calculate the moles of CuSO4路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 鈮� 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.
04

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}} 鈮� 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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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) 鈮� 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路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鈥檚 a foundational concept in stoichiometry, which allows you to predict products and reactants in given chemical reactions.

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Most popular questions from this chapter

Water "softeners" remove metal ions such as \(\mathrm{Ca}^{2+}\) and \(\mathrm{Fe}^{3+}\) by replacing them with enough \(\mathrm{Na}^{+}\) ions to maintain the same number of positive charges in the solution. If \(1.0 \times 10^{3} \mathrm{~L}\) of "hard" water is \(0.015 \mathrm{M} \mathrm{Ca}^{2+}\) and \(0.0010 \mathrm{M} \mathrm{Fe}^{3+},\) how many moles of \(\mathrm{Na}^{+}\) are needed to replace these ions?

The active compound in Pepto-Bismol contains \(\mathrm{C}, \mathrm{H}, \mathrm{O},\) and \(\mathrm{Bi} .\) (a) When \(0.22105 \mathrm{~g}\) of the compound was burned in excess \(\mathrm{O}_{2}\), \(0.1422 \mathrm{~g}\) of bismuth(III) oxide, \(0.1880 \mathrm{~g}\) of carbon dioxide, and \(0.02750 \mathrm{~g}\) of water were formed. What is the empirical formula of the compound? (b) Given a molar mass of \(1086 \mathrm{~g} / \mathrm{mol}\), determine the molecular formula. (c) Complete and balance the acid-base reaction between bismuth(III) hydroxide and salicylic acid \(\left(\mathrm{HC}_{7} \mathrm{H}_{5} \mathrm{O}_{3}\right),\) which is used to form this compound. (d) A dose of Pepto-Bismol contains \(0.600 \mathrm{mg}\) of active ingredient. If the yield of the reaction in part (c) is \(88.0 \%,\) what mass (in \(\mathrm{mg}\) ) of bismuth(III) hydroxide is required to prepare one dose?

(a) Name three common weak acids. (b) Name one common weak base. (c) What is the major difference between a weak acid and a strong acid or between a weak base and a strong base, and what experiment would you perform to observe it?

What must be present in an aqueous solution for it to conduct an electric current? What general classes of compounds form solutions that conduct?

In which of the following equations does sulfuric acid act as an oxidizing agent? In which does it act as an acid? Explain. $$ \begin{array}{l} \text { (a) } 4 \mathrm{H}^{+}(a q)+\mathrm{SO}_{4}^{2-}(a q)+2 \mathrm{NaI}(s) \longrightarrow \\ \quad 2 \mathrm{Na}^{+}(a q)+\mathrm{I}_{2}(s)+\mathrm{SO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(I) \\ \text { (b) } \mathrm{BaF}_{2}(s)+2 \mathrm{H}^{+}(a q)+\mathrm{SO}_{4}^{2-}(a q) \longrightarrow 2 \mathrm{HF}(a q)+\mathrm{BaSO}_{4}(s) \end{array} $$
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