Question

The molar heats of fusion and vaporization for silver are 11.3 \(\mathrm{kJ} / \mathrm{mol}\) and \(250 . \mathrm{kJ} / \mathrm{mol},\) respectively. Silver's normal melting point is 962 \({ }^{\circ} \mathrm{C}\), and its normal boiling point is 2212 \({ }^{\circ} \mathrm{C}\). What quantity of heat is required to melt \(12.5 \mathrm{~g}\) of silver at 962 \({ }^{\circ} \mathrm{C}\) ? What quantity of heat is liberated when \(4.59 \mathrm{~g}\) of silver vapor condenses at 2212 \({ }^{\circ} \mathrm{C}\) ?

Short answer

To melt 12.5g of silver at 962°C, 1.31 kJ of heat is required. When 4.59g of silver vapor condenses at 2212°C, 10.67 kJ of heat is liberated.

Step-by-step solution

Calculate the number of moles of silver in 12.5g and 4.59g

We will use the following formula to calculate the number of moles: \(n = \frac{m}{M}\) where \(n\) is the number of moles, \(m\) is the mass, and \(M\) is the molar mass of silver. Silver has a molar mass of 107.87 g/mol. For 12.5g of silver: \(n = \frac{12.5}{107.87}\) For 4.59g of silver: \(n = \frac{4.59}{107.87}\)

Calculate the heat required to melt 12.5g of silver at 962°C

Given the molar heat of fusion for silver is 11.3 kJ/mol, substitute the values found in step 1 into the heat formula: \(q = n \times \Delta H_{fusion}\) \(q = \frac{12.5}{107.87} \times 11.3\) Calculate the value of \(q\), the heat required.

Calculate the heat liberated when 4.59g of silver vapor condenses at 2212°C

Given the molar heat of vaporization for silver is 250 kJ/mol, substitute the values found in step 1 into the heat formula: \(q = n \times \Delta H_{vaporization}\) \(q = \frac{4.59}{107.87} \times 250\) Calculate the value of \(q\), the heat liberated. Always remember that the process of condensation releases energy; therefore the heat liberated value should be positive.

Key concepts

Thermochemistry

Thermochemistry studies the heat energy associated with chemical reactions and physical transformations, such as phase changes. When considering the melting of silver, we focus on the molar heat of fusion, the amount of energy required to convert one mole of solid into its liquid phase at the substance's melting point without changing the temperature.

The molar heat of fusion for silver is measured as 11.3 kJ/mol. To determine the total amount of heat required to melt a given quantity of silver, we apply this molar heat of fusion in a simple calculation. For instance, melting 12.5g of silver involves dividing the mass of silver by its molar mass to find the number of moles, then multiplying by the molar heat of fusion. This insight into thermochemistry allows students to grasp the direct relationship between the amount of a substance and the energy involved in its phase change.

Phase Change Calculations

Calculating the energy involved in phase changes is crucial for understanding material properties and chemical processes. Each substance has specific molar heats of fusion and vaporization reflecting the energy needed for phase transitions. These phase changes are endothermic or exothermic processes, meaning they either absorb or release heat.

For example, the melting of silver at 962°C requires heat absorption, while condensation of silver vapor at 2212°C releases heat. By calculating the moles of silver involved and accessing its specific heat values for fusion and vaporization, we determine the total heat exchange. The accurate computation of these values is essential in applications ranging from industrial processes to the design of cooling and heating systems.

Chemical Thermodynamics

Chemical thermodynamics addresses the quantitative relationship between heat exchange and chemical reactions, considering the principles of energy conservation and conversion. It explains not only how much heat is absorbed or released during a phase change but also the directionality of heat flow and how it affects the spontaneity of physical and chemical processes.

For the given exercises, understanding chemical thermodynamics helps explain why melting requires energy input (endothermic process), whereas condensation releases energy (exothermic process). The calculations for the heat required to melt silver, or the heat released when silver vapor condenses, embody the application of thermodynamic principles to practical problems, providing a deeper comprehension of the energy interactions during phase changes.