Enthalpy Change Of Dissolution Calculation For Potassium Hydroxide (KOH)

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Introduction

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The process of dissolving a solute in a solvent can either release heat (exothermic) or absorb heat (endothermic). This heat change is known as the enthalpy of dissolution, a crucial thermodynamic parameter in chemistry. Understanding the enthalpy of dissolution helps us predict the heat effects associated with various chemical processes, especially in solution chemistry. In this article, we will delve into how to calculate the enthalpy change of dissolution for potassium hydroxide ($KOH$) using experimental data. We will analyze a scenario where a student dissolves 10.4 g of $KOH$ in 250 g of water in a well-insulated open cup, observing a temperature rise from $20.0^{\circ} C$ to $27.8^{\circ} C$ over 8.4 minutes. By applying principles of calorimetry and thermochemistry, we will determine whether this process is exothermic or endothermic and quantify the heat released or absorbed.

Experimental Setup and Observations

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The experimental setup involves dissolving 10.4 g of potassium hydroxide ($KOH$) in 250 g of water within a well-insulated open cup. The initial temperature of the water is recorded as $20.0^{\circ} C$. Upon dissolution of $KOH$, the temperature rises to $27.8^{\circ} C$ over a span of 8.4 minutes. This temperature increase indicates that the dissolution process releases heat, suggesting it is an exothermic reaction. The insulation of the cup is crucial in minimizing heat exchange with the surroundings, ensuring that the observed temperature change is primarily due to the heat of dissolution. Accurate measurements of mass, temperature, and time are essential for calculating the enthalpy change of dissolution. These observations form the basis for our calculations, allowing us to quantify the heat evolved during the dissolution process and determine the enthalpy change per mole of $KOH$.

Key Concepts and Formulas

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Heat Transfer (q)

At the core of calculating the enthalpy change of dissolution lies the concept of heat transfer, denoted as q. Heat transfer represents the energy exchanged between a system and its surroundings due to a temperature difference. In calorimetry, we often use the formula:

$$q = mc\Delta T$$

Where:

• q is the heat transferred (in Joules)
• m is the mass of the substance (in grams)
• c is the specific heat capacity of the substance (in J/g°C)
• $\Delta T$ is the change in temperature (in °C), calculated as $T_{final} - T_{initial}$

This formula allows us to quantify the amount of heat absorbed or released by a substance based on its mass, specific heat capacity, and temperature change. In the context of dissolution, q represents the heat either released into the solution (exothermic process) or absorbed from the solution (endothermic process).

Molar Mass of Potassium Hydroxide (KOH)

The molar mass of a compound is the mass of one mole of its molecules or formula units. To calculate the enthalpy change on a molar basis, we need the molar mass of potassium hydroxide ($KOH$). Potassium ($K$) has an atomic mass of approximately 39.10 g/mol, oxygen ($O$) has an atomic mass of approximately 16.00 g/mol, and hydrogen ($H$) has an atomic mass of approximately 1.01 g/mol. Therefore, the molar mass of $KOH$ is:

$$Molar\ Mass\ (KOH) = 39.10\ g/mol + 16.00\ g/mol + 1.01\ g/mol = 56.11\ g/mol$$

Knowing the molar mass is crucial for converting the heat change from the experimental setup to a molar enthalpy change, which is a standard measure for comparing the heat effects of different chemical reactions.

Enthalpy Change of Dissolution ($\Delta H_{dissolution}$)

The enthalpy change of dissolution, denoted as $\Delta H_{dissolution}$, is the heat absorbed or released when one mole of a substance dissolves in a solvent at constant pressure. It is a crucial thermodynamic parameter that characterizes the energy changes associated with the dissolution process. The enthalpy change of dissolution is calculated using the formula:

$$\Delta H_{dissolution} = -\frac{q}{n}$$

Where:

• $\Delta H_{dissolution}$ is the enthalpy change of dissolution (in J/mol or kJ/mol)
• q is the heat transferred (in Joules)
• n is the number of moles of the solute dissolved

The negative sign in the formula is crucial because it accounts for the convention that heat released (exothermic, q is negative) results in a negative $\Delta H_{dissolution}$, and heat absorbed (endothermic, q is positive) results in a positive $\Delta H_{dissolution}$. By calculating $\Delta H_{dissolution}$, we can quantify the energy change per mole of solute, providing a standardized measure of the heat effect of dissolution.

Step-by-Step Calculation

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Step 1: Calculate the Heat Transferred (q)

First, we calculate the heat transferred using the formula $q = mc\Delta T$. Given:

• Mass of water, $m = 250\ g$
• Specific heat capacity of water, $c = 4.184\ J/g^{\circ}C$
• Change in temperature, $\Delta T = 27.8^{\circ}C - 20.0^{\circ}C = 7.8^{\circ}C$

$$q = (250\ g) \times (4.184\ J/g^{\circ}C) \times (7.8^{\circ}C) = 8158.8\ J$$

Therefore, the heat released into the water is 8158.8 J.

Step 2: Calculate the Number of Moles of KOH

Next, we calculate the number of moles of $KOH$ dissolved. Given:

• Mass of $KOH$ dissolved = 10.4 g
• Molar mass of $KOH$ = 56.11 g/mol

$$n = \frac{Mass}{Molar\ Mass} = \frac{10.4\ g}{56.11\ g/mol} = 0.185\ mol$$

Thus, 0.185 moles of $KOH$ were dissolved.

Step 3: Calculate the Enthalpy Change of Dissolution ($\Delta H_{dissolution}$)

Now, we calculate the enthalpy change of dissolution using the formula $\Delta H_{dissolution} = -\frac{q}{n}$.

$$\Delta H_{dissolution} = -\frac{8158.8\ J}{0.185\ mol} = -44101.62\ J/mol$$

Converting to kJ/mol:

$$\Delta H_{dissolution} = -44.10\ kJ/mol$$

Therefore, the enthalpy change of dissolution for $KOH$ is -44.10 kJ/mol, indicating an exothermic process.

Interpretation of Results

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The calculated enthalpy change of dissolution for potassium hydroxide ($KOH$) is -44.10 kJ/mol. This negative value signifies that the dissolution of $KOH$ in water is an exothermic process. In exothermic reactions, heat is released into the surroundings, resulting in an increase in the temperature of the solution. The magnitude of the enthalpy change indicates the amount of heat released per mole of $KOH$ dissolved. In this case, 44.10 kJ of heat is released when one mole of $KOH$ dissolves in water.

Significance of the Enthalpy Change

The enthalpy change of dissolution provides valuable information about the energy dynamics of the dissolution process. A large negative value, as observed here, indicates a highly exothermic reaction, which can have practical implications in various applications. For instance, the dissolution of $KOH$ is often used in applications where heat generation is required, such as in certain types of chemical heaters or reactions where maintaining a specific temperature is crucial. Understanding the enthalpy change allows for better control and prediction of the thermal effects in chemical processes.

Comparison with Literature Values

Comparing the calculated enthalpy change with literature values can validate the experimental results and provide further context. The literature value for the enthalpy of dissolution of $KOH$ is approximately -57.2 kJ/mol. The difference between our calculated value (-44.10 kJ/mol) and the literature value can be attributed to several factors, including experimental errors, heat loss to the surroundings despite insulation, and variations in the initial conditions (e.g., temperature and concentration). Despite the discrepancy, the experiment clearly demonstrates the exothermic nature of $KOH$ dissolution.

Factors Affecting Enthalpy of Dissolution

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The enthalpy of dissolution is influenced by several factors, including the nature of the solute and solvent, temperature, and pressure. Understanding these factors is crucial for predicting and controlling the heat effects associated with dissolution processes.

Solute and Solvent Interactions

The interactions between solute and solvent molecules play a significant role in determining the enthalpy of dissolution. The dissolution process involves breaking solute-solute interactions and solvent-solvent interactions, and forming solute-solvent interactions. If the energy released in forming solute-solvent interactions is greater than the energy required to break solute-solute and solvent-solvent interactions, the dissolution is exothermic ($\Delta H_{dissolution}$ < 0). Conversely, if more energy is required to break the initial interactions than is released in forming new ones, the dissolution is endothermic ($\Delta H_{dissolution}$ > 0). For $KOH$, a strong base, the strong interactions with water molecules lead to a significant release of heat.

Temperature

Temperature can affect the solubility of a solute and, consequently, the enthalpy of dissolution. Generally, the solubility of solids increases with temperature, although this is not always the case. The enthalpy of dissolution can also change with temperature, though this effect is typically smaller compared to the impact of solute-solvent interactions. According to Le Chatelier's principle, increasing the temperature will favor the endothermic process. Therefore, for an exothermic dissolution, increasing the temperature may slightly reduce the amount of heat released.

Pressure

Pressure has a minimal effect on the enthalpy of dissolution for solid and liquid solutes. However, for gaseous solutes, pressure plays a more significant role. According to Henry's Law, the solubility of a gas in a liquid is directly proportional to the pressure of the gas above the solution. Increasing the pressure of a gas over a solution will increase the amount of gas that dissolves, potentially affecting the overall enthalpy change.

Potential Sources of Error

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In experimental measurements, several potential sources of error can affect the accuracy of the results. Identifying and minimizing these errors is essential for obtaining reliable data. In the context of determining the enthalpy change of dissolution, common sources of error include:

Heat Loss to the Surroundings

Despite using a well-insulated cup, some heat loss to the surroundings is inevitable. This heat loss can lead to an underestimation of the temperature change and, consequently, the heat transferred during the dissolution process. Improving insulation, using a calorimeter specifically designed for accurate heat measurements, or applying a cooling correction can minimize this error.

Inaccurate Temperature Measurements

Temperature measurements are crucial in calorimetry experiments. Inaccurate readings from the thermometer can lead to errors in the calculated heat transfer. Calibration of the thermometer and ensuring proper immersion in the solution are essential for accurate temperature readings. Additionally, using a digital thermometer with higher precision can reduce measurement errors.

Incomplete Dissolution

If the solute does not fully dissolve in the solvent, the measured temperature change may not accurately represent the enthalpy of dissolution for the given amount of solute. Ensuring complete dissolution by stirring the mixture thoroughly and allowing sufficient time for the process to occur is crucial. Visual inspection of the solution can help confirm complete dissolution.

Measurement Errors of Mass and Volume

Inaccurate measurements of the mass of solute and solvent can also lead to errors in the final result. Using a calibrated balance and volumetric glassware can minimize these errors. It is important to measure the mass of the solute and solvent accurately to ensure precise calculations of molarity and heat transfer.

Specific Heat Capacity Variations

The specific heat capacity of the solution may vary slightly with temperature and concentration. While the specific heat capacity of water is often used as an approximation, a more accurate calculation might require considering the specific heat capacity of the solution itself. However, this effect is generally small unless high concentrations of solute are used.

Conclusion

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The experiment demonstrated the exothermic nature of the dissolution of potassium hydroxide ($KOH$) in water, with a calculated enthalpy change of dissolution of -44.10 kJ/mol. This value indicates that a significant amount of heat is released when $KOH$ dissolves, highlighting the strong interactions between $KOH$ and water molecules. Understanding the enthalpy change of dissolution is crucial for predicting and controlling the thermal effects associated with chemical processes in solution. By carefully applying principles of calorimetry and considering potential sources of error, we can accurately quantify the heat evolved during dissolution processes.

Future experiments could focus on minimizing heat loss and using more precise temperature measurements to refine the results. Additionally, exploring the effects of different concentrations and temperatures on the enthalpy of dissolution can provide a more comprehensive understanding of the thermodynamics of $KOH$ dissolution. Ultimately, such studies contribute to a deeper understanding of solution chemistry and its applications in various fields.