Question

Which compound, \(\mathrm{NaCl}, \mathrm{PCl}_{3}, \mathrm{CaCl}_{2}\), or \(\mathrm{HClO}_{2}\), contains the most chlorine atoms (or ions) in a \(100.0\)-g sample?

Short answer

The compound \(PCl_3\) contains the most chlorine atoms (or ions) in a \(100.0\)-g sample.

Step-by-step solution

Calculate Molar Masses

Calculate the molar mass for each compound by adding up the atomic masses of each element in the compound. The atomic masses of the elements, in g/mol, are approximately: \(Na = 22.99\), \(Cl = 35.45\), \(P = 30.97\), \(Ca = 40.08\), \(H = 1.01\), and \(O = 16.00\). Hence, molar masses are: \(NaCl = 22.99 + 35.45 = 58.44\ g/mol\), \(PCl_3 = 30.97 + 3(35.45) = 137.32\ g/mol\), \(CaCl_2 = 40.08 + 2(35.45) = 110.98\ g/mol\), \(HClO_2 = 1.01 + 35.45 + 2(16.00) = 68.46\ g/mol\).

Calculate Moles of Chlorine

Calculate the number of moles of chlorine in a 100-g sample each compound. From the definition of molar mass, we know that \(1\ mol\) of a substance is equivalent to its molar mass in grams. Hence, the number of moles of each compound in a \(100\ g\) sample is obtained by dividing \(100\ g\) by the molar mass of the compound. We then multiply the number of moles of each compound by the number of chlorine atoms (or ions) per molecule (or formula unit) of the compound to find the total number of moles of chlorine in each sample. For \(NaCl\), there is \(1\ mol\) of Cl for every mol of \(NaCl\), for \(PCl_3\), there are \(3\ moles\) of Cl for every mole of \(PCl_3\), for \(CaCl_2\), there are \(2\ moles\) of Cl for every mole of \(CaCl_2\) and for \(HClO_2\), there is \(1\ mole\) of Cl for every mole of \(HClO_2\).

Identify the Sample with Most Moles of Chlorine

The sample that has the highest number of moles of chlorine will, consequently, contain the highest number of chlorine atoms (or ions). This is because each mole represents exactly the same number of particles (in this case, atoms or ions), namely Avogadro’s number, \(6.02 × 10^{23}\). So now identify the sample with the highest number of moles of chlorine computed from the previous step.

Key concepts

Molar Mass Calculation

To find out how much of each element is in a compound, we need to calculate the molar mass. Molar mass is the weight of one mole of a substance in grams per mole (g/mol). To get the molar mass, you add up the atomic masses of all the atoms in the compound. Here’s how you can do it for some common compounds:

• For NaCl (table salt), add the atomic masses of sodium (Na) and chlorine (Cl):\[\text{NaCl} = 22.99 + 35.45 = 58.44\ g/mol\]
• For PCl₃, add the atomic mass of phosphorus (P) and three times the atomic mass of Cl:\[\text{PCl}_3 = 30.97 + 3(35.45) = 137.32\ g/mol\]
• For CaCl₂, add the atomic mass of calcium (Ca) and twice the atomic mass of Cl:\[\text{CaCl}_2 = 40.08 + 2(35.45) = 110.98\ g/mol\]
• For HClO₂, add the atomic masses of hydrogen (H), Cl, and two oxygens (O):\[\text{HClO}_2 = 1.01 + 35.45 + 2(16.00) = 68.46\ g/mol\]

By understanding molar mass, you can find out how many moles are in a given sample and compare the content of different compounds.

Chemical Formulas

Chemical formulas tell you what atoms and how many of each are in a compound. They are shorthand ways of showing the elements and their quantities. For example:

• NaCl: This formula means there is one sodium atom and one chlorine atom.
• PCl₃: This one has one phosphorus atom and three chlorine atoms.
• CaCl₂: Here, you have one calcium atom and two chlorine atoms.
• HClO₂: It contains one hydrogen atom, one chlorine atom, and two oxygen atoms.

These formulas help you know how much of each element you'll have when you have one mole of the compound. Understanding the formula is your first step in calculating other properties, like molar mass and moles of individual atoms or ions. This is crucial when comparing amounts of specific atoms across different compounds.

Avogadro's Number

Avogadro's Number, \(6.02 \times 10^{23}\), is a very large number that represents the number of atoms, ions, or molecules in a mole of a substance. This concept helps bridge the micro world of atoms with the macro world we can measure.
This means if you have one mole of chlorine atoms, you actually have \(6.02 \times 10^{23}\) chlorine atoms. This number helps you understand how incredibly small atoms are, but also how they add up substantially in terms of weight you can measure. For solving problems like comparing chlorine content in compounds, Avogadro's number is vital. You calculate moles based on molar mass and then relate it to atoms using Avogadro’s number. Understanding this concept makes it easier to bridge the gap between moles of substance and the actual amount of atoms or ions you have.