Problem 79
Question
Most pasta recipes instruct you to add a teaspoon of salt to a pot of boiling water. Does this have a significant effect on the boiling temperature? Justify your answer with a rough numerical estimate.
Step-by-Step Solution
Verified Answer
Adding a teaspoon of salt slightly raises the boiling point, but the change (0.088 °C) is insignificant.
1Step 1: Understand the Chemistry
When salt (NaCl) is added to water, it dissociates into sodium (Na⁺) and chloride (Cl⁻) ions. This increases the boiling point of the water due to a phenomenon called boiling point elevation.
2Step 2: Know the Formula
The boiling point elevation can be estimated by the formula \(\Delta T_b = i \cdot K_b \cdot m\)where \(\Delta T_b\) is the change in boiling temperature, \(i\) is the Van't Hoff factor (i=2 for NaCl), \(K_b\) is the ebullioscopic constant of water (0.512 °C·kg/mol), and \(m\) is the molality of the solution.
3Step 3: Calculate the Molality
A teaspoon of salt is approximately 5 grams. The molar mass of NaCl is 58.44 g/mol, so the number of moles of salt is \(\frac{5 \text{ g}}{58.44 \text{ g/mol}} \approx 0.086 \, \text{mol}\).Assuming you add this to 1 kg of water (roughly 1 liter), the molality \(m\) is 0.086 mol/kg.
4Step 4: Compute the Boiling Point Elevation
With the given formula, substitute in the values:\(\Delta T_b = 2 \cdot 0.512 \text{ °C·kg/mol} \cdot 0.086 \text{ mol/kg} \approx 0.088 \text{ °C}\).This means the boiling point of the water increases by approximately 0.088 °C.
5Step 5: Analyze the Result
The typical boiling point of water is 100 °C. A 0.088 °C increase is very small, which indicates that adding a teaspoon of salt has a negligible effect on the boiling temperature.
Key Concepts
Van't Hoff FactorEbullioscopic ConstantMolalityBoiling Temperature
Van't Hoff Factor
The Van't Hoff factor, denoted as 'i', is a crucial element in understanding boiling point elevation. It represents the number of particles a compound dissociates into in solution. For ionic compounds like salt (NaCl), the Van't Hoff factor is greater than one due to dissociation.
NaCl dissociates into two ions: sodium (Na⁺) and chloride (Cl⁻). Hence, the Van't Hoff factor for NaCl is 2.
This factor plays an active role in calculating colligative properties such as boiling point elevation.
Without this factor, we wouldn't be able to accurately reflect the increased number of solute particles in a solution. For ionic compounds, especially, the Van't Hoff factor is indispensable in formulae that determine changes in boiling and freezing points.
NaCl dissociates into two ions: sodium (Na⁺) and chloride (Cl⁻). Hence, the Van't Hoff factor for NaCl is 2.
This factor plays an active role in calculating colligative properties such as boiling point elevation.
Without this factor, we wouldn't be able to accurately reflect the increased number of solute particles in a solution. For ionic compounds, especially, the Van't Hoff factor is indispensable in formulae that determine changes in boiling and freezing points.
Ebullioscopic Constant
The ebullioscopic constant, symbolized as \(K_b\), is intrinsic to every solvent and provides the necessary relationship between the increase in boiling point and the molality of the solution. This constant is unique to each solvent; for water, \(K_b\) is 0.512 °C·kg/mol.
It specifically helps us understand how much the boiling point of a solvent will increase when a solute is added.
This addition occurs on a per molal basis, calculated using the molality of the solution.
When evaluating boiling point changes, this constant ensures that we account for the physical properties of the solvent itself, not just the solute's impact.
It specifically helps us understand how much the boiling point of a solvent will increase when a solute is added.
This addition occurs on a per molal basis, calculated using the molality of the solution.
When evaluating boiling point changes, this constant ensures that we account for the physical properties of the solvent itself, not just the solute's impact.
Molality
Molality, indicated by \(m\), measures the concentration of a solute in a solution. It is defined as moles of solute per kilogram of solvent.
This differs from molarity, which is based on the volume of the solution.
To determine molality in our example, we first need the moles of salt, calculated from its mass and molar mass. A teaspoon of salt weighing approximately 5 grams equates to about 0.086 moles.
By dividing by 1 kg of water, we find the molality to be 0.086 mol/kg.
Molality is particularly useful for colligative properties like boiling point elevation because it remains unaffected by temperature changes.
This differs from molarity, which is based on the volume of the solution.
To determine molality in our example, we first need the moles of salt, calculated from its mass and molar mass. A teaspoon of salt weighing approximately 5 grams equates to about 0.086 moles.
By dividing by 1 kg of water, we find the molality to be 0.086 mol/kg.
Molality is particularly useful for colligative properties like boiling point elevation because it remains unaffected by temperature changes.
Boiling Temperature
Boiling temperature refers to the point at which a liquid turns into vapor. This temperature is influenced by the addition of solutes.
With the concept of boiling point elevation, the presence of a solute, like salt, raises the boiling temperature of the solvent.
However, the degree of change depends on factors like the Van't Hoff factor, molality, and the ebullioscopic constant.
In our case, adding a teaspoon of salt raises the boiling point of water by roughly 0.088 °C.
While significant in theory, this small change has limited practical effect when cooking, as it does not substantially alter cooking times or conditions.
With the concept of boiling point elevation, the presence of a solute, like salt, raises the boiling temperature of the solvent.
However, the degree of change depends on factors like the Van't Hoff factor, molality, and the ebullioscopic constant.
In our case, adding a teaspoon of salt raises the boiling point of water by roughly 0.088 °C.
While significant in theory, this small change has limited practical effect when cooking, as it does not substantially alter cooking times or conditions.
Other exercises in this chapter
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