Question

Calculate the boiling temperature and freezing temperature at 1 atmosphere pressure of a solution formed by dissolving 123 grams of ferrous oxide in 1.890 grams of HCl.

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Jon

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To calculate the boiling and freezing temperatures of a solution, we need to use the concept of colligative properties. These properties depend on the number of solute particles present in the solution, regardless of their nature.

Step 1: Calculate the moles of the solute particles

First, we need to find the moles of both ferrous oxide (FeO) and hydrochloric acid (HCl) present in the solution.

The molar mass of FeO is 71.85 g/mol, so the moles of FeO can be calculated as follows:

\text{Moles of FeO} = \frac{\text{Mass of FeO}}{\text{Molar Mass of FeO}} = \frac{123 \, \text{g}}{71.85 \, \text{g/mol}}

The molar mass of HCl is 36.46 g/mol, so the moles of HCl can be calculated as follows:

\text{Moles of HCl} = \frac{\text{Mass of HCl}}{\text{Molar Mass of HCl}} = \frac{1.890 \, \text{g}}{36.46 \, \text{g/mol}}

Step 2: Calculate the total moles of solute particles

Since FeO dissociates into Fe^2+ and O^2-, and HCl dissociates into H^+ and Cl^-, we need to multiply the moles by their respective coefficients of dissociation.

The dissociation coefficient for FeO is 1, and for HCl it is 2 (one mole of HCl produces two moles of ions). Therefore, the total moles of solute particles (N) is given by:

N = \text{Moles of FeO} \times \text{Dissociation coefficient of FeO} + \text{Moles of HCl} \times \text{Dissociation coefficient of HCl}

Step 3: Calculate the boiling temperature elevation using the van't Hoff factor

The boiling temperature elevation (ΔT_boil) is given by the formula:

\Delta T_{\text{boil}} = K_{\text{boil}} \times b \times N

where K_{\text{boil}} is the boiling point elevation constant for the solvent and b is the molality of the solute particles.

Step 4: Calculate the freezing temperature depression using the van't Hoff factor

The freezing temperature depression (ΔT_freeze) is given by the formula:

\Delta T_{\text{freeze}} = K_{\text{freeze}} \times b \times N

where K_{\text{freeze}} is the freezing point depression constant for the solvent.

Step 5: Calculate the boiling temperature and freezing temperature of the solution

Finally, we can calculate the boiling and freezing temperatures of the solution using the equations:

\text{Boiling Temperature} = \text{Boiling Point of Pure Solvent} + \Delta T_{\text{boil}}

\text{Freezing Temperature} = \text{Freezing Point of Pure Solvent} - \Delta T_{\text{freeze}}

Answer:

The boiling temperature and freezing temperature of the solution can be calculated using the given data and the above equations.

Step 1: Calculate the moles of the solute particles

First, we need to find the moles of both ferrous oxide (FeO) and hydrochloric acid (HCl) present in the solution.

The molar mass of FeO is 71.85 g/mol, so the moles of FeO can be calculated as follows:

The molar mass of HCl is 36.46 g/mol, so the moles of HCl can be calculated as follows:

Step 2: Calculate the total moles of solute particles

Since FeO dissociates into Fe^2+ and O^2-, and HCl dissociates into H^+ and Cl^-, we need to multiply the moles by their respective coefficients of dissociation.

The dissociation coefficient for FeO is 1, and for HCl it is 2 (one mole of HCl produces two moles of ions). Therefore, the total moles of solute particles (N) is given by:

Step 3: Calculate the boiling temperature elevation using the van't Hoff factor

The boiling temperature elevation (ΔT_boil) is given by the formula:

where

Step 4: Calculate the freezing temperature depression using the van't Hoff factor

The freezing temperature depression (ΔT_freeze) is given by the formula:

where

Step 5: Calculate the boiling temperature and freezing temperature of the solution

Finally, we can calculate the boiling and freezing temperatures of the solution using the equations:

Answer:

The boiling temperature and freezing temperature of the solution can be calculated using the given data and the above equations.

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