Suppose that 0.95 g of water condenses on a 75.0-g block of iron that is initially at 22 °C. If the heat released during condensation goes only to warming the iron block, what is the final temperature (in °C) of the iron block? (Assume a constant enthalpy of vaporization for water of 44.0 kJ/mol.)

Verified step by step guidance

1. Calculate the number of moles of water that condense using the formula: \( n = \frac{\text{mass}}{\text{molar mass}} \). The molar mass of water is 18.02 \( \text{g/mol} \).
2. Determine the heat released during condensation using the formula: \( q = n \times \Delta H_{\text{vap}} \), where \( \Delta H_{\text{vap}} \) is the enthalpy of vaporization (44.0 kJ/mol).
3. Convert the heat released from kJ to J by multiplying by 1000, since 1 kJ = 1000 J.
4. Use the formula for heat transfer to the iron block: \( q = m \times c \times \Delta T \), where \( m \) is the mass of the iron block, \( c \) is the specific heat capacity of iron (0.449 J/g°C), and \( \Delta T \) is the change in temperature.
5. Solve for the final temperature \( T_f \) of the iron block by rearranging the equation: \( \Delta T = \frac{q}{m \times c} \) and adding the initial temperature of the iron block (22 °C) to \( \Delta T \).

Key Concepts

Heat Transfer

Heat transfer is the process by which thermal energy moves from one object to another due to a temperature difference. In this scenario, the heat released from the condensation of water is transferred to the iron block, causing its temperature to rise. Understanding the principles of heat transfer is essential for calculating the final temperature of the iron.

Enthalpy of Vaporization

The enthalpy of vaporization is the amount of energy required to convert a unit mass of a substance from liquid to gas at constant temperature and pressure. For water, this value is given as 44.0 kJ/mol, which indicates the energy released when water vapor condenses into liquid. This concept is crucial for determining the total heat released during the condensation process.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. For the iron block, knowing its specific heat capacity allows us to calculate how much its temperature will increase when it absorbs the heat released from the condensing water. This relationship is key to finding the final temperature of the iron.