Problem 114 - Chemistry and Chemical Reactivity

Question

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 \(\mathrm{BaSO}_{4}\)

Step-by-Step Solution

Answer

BeCl2 has the largest number of ions.

Step 1: 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 \( \text{BaSO}_4 = 137.33 + 32.07 + 4(16.00) = 233.39 \, \text{g/mol} \)

Step 2: 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 \( \text{BaSO}_4 \): \( \frac{1.0}{233.39} = 0.0043 \, \text{moles} \)

Step 3: 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.

Step 4: 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.

Key Concepts

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.