Question

Instant hot packs contain a solid and a pouch of water. When the pack is squeezed, the pouch breaks and the solid dissolves, increasing the temperature because of the exothermic reaction. The following reaction is used to make a hot pack: $$\mathrm{LiCl}(s) \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \mathrm{Li}^{+}(a q)+\mathrm{Cl}^{-}(a q) \quad \Delta H=-36.9 \mathrm{~kJ}$$ What is the final temperature in a squeezed hot pack that contains \(25.0 \mathrm{~g}\) of \(\mathrm{LiCl}\) dissolved in \(125 \mathrm{~mL}\) of water? Assume a specific heat of \(4.18 \mathrm{~J} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)\) for the solution, an initial temperature of \(25.0{ }^{\circ} \mathrm{C}\), and no heat transfer between the hot pack and the environment.

Short answer

The final temperature is 59.8°C.

Step-by-step solution

Determine moles of LiCl

First, convert the mass of \( \mathrm{LiCl} \) into moles. The molar mass of \( \mathrm{LiCl} \) is approximately \( 6.94 + 35.45 = 42.39 \, \mathrm{g/mol} \). Using the formula, \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \), calculate the moles of \( \mathrm{LiCl} \): \[ \text{moles of } \mathrm{LiCl} = \frac{25.0 \, \text{g}}{42.39 \, \text{g/mol}} \approx 0.590 \, \text{mol} \]

Calculate heat released

Use the change in enthalpy \( \Delta H \) to find the heat released during the reaction. The reaction releases \(-36.9 \, \text{kJ/mol} \) for every mole of \( \mathrm{LiCl} \). The heat \( q \) released by the reaction is calculated by multiplying \( \Delta H \) by the number of moles: \[ q = -36.9 \, \text{kJ/mol} \times 0.590 \, \text{mol} = -21.8 \, \text{kJ} \] Convert the heat to Joules: \[ q = -21.8 \, \text{kJ} \times 1000 \, \text{J/kJ} = -21800 \, \text{J} \]

Calculate mass of the solution

The total mass of the solution is the sum of the mass of \( \mathrm{LiCl} \) and the mass of water (since 125 mL of water has a mass of approximately 125 g): \[ \text{Mass of solution} = 25.0 \, \text{g} + 125 \, \text{g} = 150 \, \text{g} \]

Calculate change in temperature

Use the formula for heat transfer \( q = mc\Delta T \) where \( m \) is the mass of the solution, \( c \) is the specific heat, and \( \Delta T \) is the change in temperature. Rearrange to solve for \( \Delta T \): \[ \Delta T = \frac{q}{mc} = \frac{-21800 \, \text{J}}{150 \, \text{g} \times 4.18 \, \text{J/g}^{\circ}\text{C}} \approx -34.8^{\circ} \text{C} \]

Calculate Final Temperature

Subtract the temperature change from the initial temperature to find the final temperature: \[ T_{\text{final}} = T_{\text{initial}} + \Delta T = 25.0^{\circ} \text{C} - 34.8^{\circ} \text{C} = -9.8^{\circ} \text{C} \] However, since this is an exothermic reaction and heat is released, the temperature actually increases. Re-evaluate the calculation as: \( T_{\text{final}} = 25.0^{\circ} \text{C} + 34.8^{\circ} \text{C} \).

Correct Final Temperature

Since the absolute change in temperature \( \Delta T \) is positive, as calculated, the final temperature should be: \[ T_{\text{final}} = 25.0^{\circ} \text{C} + 34.8^{\circ} \text{C} = 59.8^{\circ} \text{C} \]

Key concepts

Thermodynamics

Thermodynamics is the branch of physical science that deals with heat and temperature and their relation to energy and work. It studies the laws governing these processes and how thermal energy is converted within systems. In an exothermic reaction like the one in the hot pack, energy is released into the surroundings.
This is an essential concept in understanding how systems reach equilibrium and how energy is conserved and transferred.
Specifically, thermodynamics provides valuable insight into how chemical reactions, such as the dissolution of lithium chloride in water, reach a higher energy state by releasing heat. This change impacts the temperature and phase of the involved substances.

Enthalpy Change

Enthalpy change (\( \Delta H \)) measures the heat content that is either absorbed or released by a system during a chemical reaction. When \( \Delta H \) is negative, as in the reaction involving \( \text{LiCl} \), it indicates that the reaction is exothermic, meaning heat is released. \[\Delta H = -36.9 \text{ kJ/mol}\]
This value tells us how much heat energy is given off for every mole of \( \text{LiCl} \) that dissolves. Knowing this energy release helps us calculate the temperature change, showing how powerful these reactions can be. It reflects the internal energy change of the system when it moves from reactants to products.

Heat Transfer

Heat transfer is the movement of thermal energy from a hotter object to a cooler one. In the context of a hot pack, the heat released by the dissolving \( \text{LiCl} \) is transferred to the surrounding water, increasing the water's temperature.
This process can be calculated using the formula \( q = mc\Delta T \), where:

• \( q \) is the heat transfer (in Joules),
• \( m \) is the mass of the substance (in grams),
• \( c \) is the specific heat capacity (how much heat per gram per degree Celsius),
• \( \Delta T \) is the change in temperature.

By using these elements, we can predict how much the temperature of the water will increase, crucial for determining the reaction's efficiency in heating.

Dissolution Process

The dissolution process involves the dissolving of a solute (solid) in a solvent (liquid) to form a solution. During this process, interactions at the molecular level occur, where solute molecules are separated and surrounded by solvent molecules.
For \( \text{LiCl} \), when dissolved in water, the crystal lattice breaks apart, and ions \( \text{Li}^+ \) and \( \text{Cl}^- \) are dispersed, releasing energy. This exothermic nature is due to stronger interactions forming between ions and water molecules than those that were in the solid form.
This process is critical as it shows how ionic compounds like \( \text{LiCl} \) can not only dissolve but also contribute significantly to the temperature rise, making them suitable for applications like instant hot packs.