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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 g of CaS (d) \(1.0 \mathrm{g}\) of \(\mathrm{SrCO}_{3}\) (e) \(1.0 \mathrm{g}\) of \(\mathrm{BaSO}_{4}\)

Short Answer

Expert verified
The sample of 1.0 g BeCl鈧 has the largest number of ions.

Step by step solution

01

Calculate the Molar Masses

First, we need to calculate the molar mass of each compound to determine how many moles are in 1 gram. - BeCl鈧: (Be) + 2*(Cl) = 9 + 2*35.5 = 80 g/mol - MgCl鈧: (Mg) + 2*(Cl) = 24 + 2*35.5 = 95 g/mol - CaS: (Ca) + (S) = 40 + 32 = 72 g/mol - SrCO鈧: (Sr) + (C) + 3*(O) = 88 + 12 + 3*16 = 148 g/mol - BaSO鈧: (Ba) + (S) + 4*(O) = 137 + 32 + 4*16 = 233 g/mol.
02

Calculate Moles in 1 Gram

For each compound, calculate the moles from 1 gram using the formula: \( moles = \frac{mass}{molar\ mass} \).- BeCl鈧: \( \frac{1.0}{80} = 0.0125 \text{ moles} \)- MgCl鈧: \( \frac{1.0}{95} = 0.01053 \text{ moles} \)- CaS: \( \frac{1.0}{72} = 0.01389 \text{ moles} \)- SrCO鈧: \( \frac{1.0}{148} = 0.00676 \text{ moles} \)- BaSO鈧: \( \frac{1.0}{233} = 0.00429 \text{ moles} \).
03

Determine Number of Ions Per Mole

Identify the number of ions per formula unit for each compound. - BeCl鈧 produces 3 ions (1 Be虏鈦 and 2 Cl鈦) - MgCl鈧 produces 3 ions (1 Mg虏鈦 and 2 Cl鈦) - CaS produces 2 ions (1 Ca虏鈦 and 1 S虏鈦) - SrCO鈧 produces 2 ions (1 Sr虏鈦 and 1 CO鈧兟测伝) - BaSO鈧 produces 2 ions (1 Ba虏鈦 and 1 SO鈧劼测伝).
04

Calculate Total Number of Ions

Multiply the moles of each compound by the number of ions per formula unit to get the total number of ions.- BeCl鈧: \( 0.0125 \times 3 = 0.0375 \text{ moles of ions} \)- MgCl鈧: \( 0.01053 \times 3 = 0.03159 \text{ moles of ions} \)- CaS: \( 0.01389 \times 2 = 0.02778 \text{ moles of ions} \)- SrCO鈧: \( 0.00676 \times 2 = 0.01352 \text{ moles of ions} \)- BaSO鈧: \( 0.00429 \times 2 = 0.00858 \text{ moles of ions} \).
05

Compare Ion Quantities

Compare the moles of ions calculated to find which sample has the largest number of ions. BeCl鈧 has 0.0375 moles of ions, the largest among the samples.

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Key Concepts

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

Molar Mass Calculation
When calculating the molar mass of a compound, we simply add up the atomic masses of all the atoms present in the compound's chemical formula. This involves looking at the periodic table to find the atomic mass of each element and then multiplying it by the number of times that element appears in the formula.

For example, in the compound beryllium chloride (BeCl鈧), we have:
  • Beryllium (Be) has an atomic mass of approximately 9 g/mol.
  • Chlorine (Cl) has an atomic mass of about 35.5 g/mol per atom, and since we have two chlorine atoms, we multiply this by 2.
Adding these together gives the molar mass of BeCl鈧: \[9 + 2 \times 35.5 = 80\,\text{g/mol}\].
This same process can be applied to other compounds. Understanding how to calculate molar mass is essential as it allows us to determine how many moles are present in a given mass of compound.
Ions in Compounds
Ionic compounds consist of positively charged ions (cations) and negatively charged ions (anions). These ions form a compound because the total positive charge balances the total negative charge, maintaining electrical neutrality.

For example, in magnesium chloride (MgCl鈧), magnesium forms a cation with a charge of +2 (Mg虏鈦), and each chlorine atom forms an anion with a charge of -1 (Cl鈦). Since there are two chloride ions needed to balance the charge of one magnesium ion, the formula is MgCl鈧.

Understanding how to identify and count the ions in compounds is crucial for various calculations in chemistry, such as finding the number of particles or charges present in a sample.
Moles of Ions
The concept of "moles of ions" relates to how many individual ions are present in a mole of an ionic compound. Once we know the number of moles of a compound we have, we can easily find the moles of ions by multiplying the moles of the compound by the number of ions produced per formula unit of the compound.

Take calcium sulfide (CaS) as an example. A mole of CaS will dissociate into a mole of Ca虏鈦 ions and a mole of S虏鈦 ions, equating to 2 moles of ions in total per mole of CaS.
In contrast, for something like magnesium chloride (MgCl鈧), one mole will produce 3 moles of ions: 1 mole of Mg虏鈦 ions and 2 moles of Cl鈦 ions. Counting these ions helps in determining the entire ion quantity in a given amount of a substance, which is pivotal in reactions and stoichiometry.
Chemical Formula Analysis
Analyzing chemical formulas involves understanding what the symbols and numbers within a formula mean. Each symbol represents an element, while subscript numbers tell you how many atoms of each element are in one molecule or formula unit of the compound.
This analysis isn't just about the numbers; it reveals the compound's nature and behavior.

For instance, in strontium carbonate (SrCO鈧), Sr stands for strontium, which doesn't have a subscript, indicating there's only one atom. CO鈧 is a polyatomic ion (carbonate) consisting of one carbon atom and three oxygen atoms.
Through chemical formula analysis, we know this compound forms two ions: one Sr虏鈦 ion and one CO鈧兟测伝 ion.
Analyzing chemical formulas helps us understand different compounds' compositions and prepares us for more complex tasks, such as calculating molar mass or determining ionic proportions.

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Most popular questions from this chapter

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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