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Chapter 2: Problem 114

Which of the following samples has the largest number of ions? (a) \(1.0 \mathrm{g}\) of \(\mathrm{BeCl}_{2}\) (b) \(1.0 \mathrm{g}\) of \(\mathrm{MgCl}_{2}\) (c) \(1.0 \mathrm{g}\) of \(\mathrm{CaS}\) (d) \(1.0 \mathrm{g}\) of \(\mathrm{SrCO}_{3}\) (e) \(1.0 \mathrm{g}\) of \(\mathrm{BaSO}_{4}\)

Short Answer

Expert verified
BeCl2 has the largest number of ions.

Step by step solution

01

Calculate Molar Mass of Each Compound

First, we need to find the molar mass of each compound. - For \( \text{BeCl}_2 \): \( \text{Be} \) is 9.01 g/mol, \( \text{Cl} \) is 35.45 g/mol, so \( \text{BeCl}_2 = 9.01 + 2(35.45) = 79.91 \, \text{g/mol} \)- For \( \text{MgCl}_2 \): \( \text{Mg} \) is 24.31 g/mol, \( \text{Cl} \) is 35.45 g/mol, so \( \text{MgCl}_2 = 24.31 + 2(35.45) = 95.21 \, \text{g/mol} \)- For \( \text{CaS} \): \( \text{Ca} \) is 40.08 g/mol, \( \text{S} \) is 32.07 g/mol, so \( \text{CaS} = 40.08 + 32.07 = 72.15 \, \text{g/mol} \)- For \( \text{SrCO}_3 \): \( \text{Sr} \) is 87.62 g/mol, \( \text{C} \) is 12.01 g/mol, \( \text{O} \) is 16.00 g/mol, so \( \text{SrCO}_3 = 87.62 + 12.01 + 3(16.00) = 147.63 \, \text{g/mol} \)- For \( \text{BaSO}_4 \): \( \text{Ba} \) is 137.33 g/mol, \( \text{S} \) is 32.07 g/mol, \( \text{O} \) is 16.00 g/mol, so \( \text{BaSO}_4 = 137.33 + 32.07 + 4(16.00) = 233.39 \, \text{g/mol} \)
02

Calculate Number of Moles in Each Sample

For each compound, divide the mass of the sample by its molar mass to find the number of moles:- For \( \text{BeCl}_2 \): \( \frac{1.0}{79.91} = 0.0125 \, \text{moles} \)- For \( \text{MgCl}_2 \): \( \frac{1.0}{95.21} = 0.0105 \, \text{moles} \)- For \( \text{CaS} \): \( \frac{1.0}{72.15} = 0.0139 \, \text{moles} \)- For \( \text{SrCO}_3 \): \( \frac{1.0}{147.63} = 0.0068 \, \text{moles} \)- For \( \text{BaSO}_4 \): \( \frac{1.0}{233.39} = 0.0043 \, \text{moles} \)
03

Determine Number of Ions Per Mole

Identify how many ions each compound dissociates into:- \( \text{BeCl}_2 \) dissociates into 3 ions: 1 Be\(^{2+}\) and 2 Cl\(^{-}\).- \( \text{MgCl}_2 \) dissociates into 3 ions: 1 Mg\(^{2+}\) and 2 Cl\(^{-}\).- \( \text{CaS} \) dissociates into 2 ions: 1 Ca\(^{2+}\) and 1 S\(^{2-}\).- \( \text{SrCO}_3 \) dissociates into 2 ions: 1 Sr\(^{2+}\) and 1 CO\(^{2-}_3\), though in reality, carbonates rarely fully dissociate into ions.- \( \text{BaSO}_4 \) does not dissociate significantly in water, it's largely insoluble.
04

Calculate Total Number of Ions in Each Sample

Multiply the moles of each sample by the number of ions it dissociates into:- For \( \text{BeCl}_2 \): \( 0.0125 \, \text{moles} \times 3 = 0.0375 \, \text{moles of ions} \)- For \( \text{MgCl}_2 \): \( 0.0105 \, \text{moles} \times 3 = 0.0315 \, \text{moles of ions} \)- For \( \text{CaS} \): \( 0.0139 \, \text{moles} \times 2 = 0.0278 \, \text{moles of ions} \)- For \( \text{SrCO}_3 \): \( 0.0068 \, \text{moles} \times 2 = 0.0136 \, \text{moles of ions} \)- \( \text{BaSO}_4 \) doesn't dissociate well, contributing negligible ions.

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Key Concepts

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

Molar Mass Calculation
Understanding molar mass is crucial in chemistry, as it helps you convert between grams and moles of a substance. The molar mass is essentially the weight of one mole of a compound, typically expressed in grams per mole (g/mol). To calculate it, you need to add up the atomic masses of all the atoms present in a molecule. For instance, in the molecule \(\text{BeCl}_2\), you add the atomic mass of one beryllium atom (9.01 g/mol) and two chlorine atoms (each 35.45 g/mol). Hence, the molar mass of \(\text{BeCl}_2\) becomes \(79.91\, \text{g/mol}\).
Knowing the molar mass allows you to figure out how many moles are in a given mass of a substance, a key step in many chemical calculations.
Ion Counting
Ion counting involves determining how many ions a compound will produce when it dissociates in solution. Different compounds break down into different numbers of ions. For example, \(\text{MgCl}_2\) produces three ions: one magnesium ion \(\text{Mg}^{2+}\) and two chloride ions \(\text{Cl}^{-}\).
This information is critical when calculating the total number of ions present in a sample, as it directly influences the overall charge balance in chemical reactions and solutions.
Dissociation of Compounds
When ionic compounds like \(\text{NaCl}\) dissolve in water, they dissociate into individual ions. Dissociation is the process in which a solid ionic compound separates into its ions. Not all compounds dissociate equally. For instance, \(\text{BaSO}_4\) is largely insoluble and doesn't dissociate in water, meaning it won't significantly contribute to the ion count.
Understanding which compounds dissociate and to what extent is essential for predicting the behavior of molecules in a solution, especially in reactions occurring in aqueous environments.
Stoichiometry
Stoichiometry is the branch of chemistry that deals with measuring the amounts of reactants and products in a chemical reaction. It often involves balancing equations and using the concept of moles to relate quantities of substances. By comparing the moles of different compounds, you can determine proportions and predict how much product will form from given reactants.
In exercises like this one, stoichiometry assists in calculating the total number of ions by using the moles of each compound and how many ions they break down into. This shows the practical application of stoichiometry in solving real-world chemical problems.

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Most popular questions from this chapter

The highest mass peaks in the mass spectrum of \(\mathrm{Br}_{2}\) occur at \(m / Z 158,160,\) and \(162 .\) The ratio of intensities of these peaks is approximately \(1: 2: 1 .\) Bromine has two stable isotopes, \(^{79} \mathrm{Br}(50.7 \% \text { abundance })\) and \(^{81} \mathrm{Br}\) \((49.3 \% \text { abundance })\) (a) What molecular species gives rise to each of these peaks? (b) Explain the relative intensities of these peaks. (Hint: Consider the probabilities of each atom combination.)

Succinic acid occurs in fungi and lichens. Its empirical formula is \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2},\) and its molar mass is \(118.1 \mathrm{g} / \mathrm{mol}\) What is its molecular formula?

An organic compound has the empirical formula \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{NO} .\) If its molar mass is \(116.1 \mathrm{g} / \mathrm{mol},\) what is the molecular formula of the compound?

A compound called MMT was once used to boost the octane rating of gasoline. What is the empirical formula of MMT if it is \(49.5 \% \mathrm{C}, 3.2 \% \mathrm{H}, 22.0 \% \mathrm{O}\) and \(25.2 \%\) Mn?

Consider an atom of \(^{64} \mathrm{Zn}\). (a) Calculate the density of the nucleus in grams per cubic centimeter, knowing that the nuclear radius is \(4.8 \times 10^{-6} \mathrm{nm}\) and the mass of the \(^{64} \mathrm{Zn}\) atom is \(1.06 \times 10^{-22} \mathrm{g} .\) (Recall that the volume of a sphere is \(\left.[4 / 3] \pi r^{3} .\right)\) (b) Calculate the density of the space occupied by the electrons in the zinc atom, given that the atomic radius is \(0.125 \mathrm{nm}\) and the electron mass is \(9.11 \times 10^{-28} \mathrm{g}\) (c) Having calculated these densities, what statement can you make about the relative densities of the parts of the atom?
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