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# 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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## Answer to a math 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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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}}

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