Constants for water
\begin{tabular}{|l|l|}
\hline$\Delta H_{\text {vap }}$ & $40.65 kJ / mol$ \\
\hline$\Delta H_{\text {f }}$ & $-285.83 kJ / mol$ \\
\hline$\Delta H_{\text {fuslon }}$ & $6.03 kJ / mol$ \\
\hline specific heat & $4.186 J / g ^{\circ} C$ \\
\hline molar mass & 18.02 g \\
\hline
\end{tabular}
How much energy is released when 6.0 g of water is condensed from water vapor?
A. $6.0 g \times 1 mol / 18.02 g \times 6.03 kJ / mol$
B. $6.0 g \times 1 mol / 18.02 g \times 40.65 kJ / mol$
C. $6.0 g \times 1 mol / 18.02 g \times 4.186 kJ / mol$
D. $6.0 g \times 1 mol / 18.02 g \times(-285.83 kJ / mol )$
Answer (2)
Convert the mass of water from grams to moles: 18.02 g/mol 6.0 g = 0.333 mol .
Multiply the number of moles by the enthalpy of vaporization: 0.333 mol × 40.65 kJ/mol = 13.53 kJ .
The energy released when 6.0 g of water is condensed from water vapor is 13.53 kJ.
The correct answer is B: 6.0 g × 1 m o l /18.02 g × 40.65 k J / m o l B
Explanation
Problem Analysis We are asked to calculate the amount of energy released when 6.0 g of water is condensed from water vapor. We are given the enthalpy of vaporization for water, which is the amount of energy required to vaporize one mole of water. Condensation is the reverse process of vaporization, so the energy released during condensation will be equal to the enthalpy of vaporization, but with a negative sign.
Convert grams to moles First, we need to convert the mass of water from grams to moles. We are given the molar mass of water as 18.02 g/mol. To convert grams to moles, we use the formula: m o l es = m o l a r ma ss ( g / m o l ) ma ss ( g ) m o l es = 18.02 g / m o l 6.0 g = 0.333 m o l
Calculate energy released Next, we use the enthalpy of vaporization to calculate the energy released during condensation. The enthalpy of vaporization is given as 40.65 kJ/mol. Since condensation is the reverse of vaporization, the energy released will be the negative of the enthalpy of vaporization. Therefore, the energy released is: E n er g y = m o l es × Δ H v a p E n er g y = 0.333 m o l × 40.65 k J / m o l = 13.53 k J
Final Answer The energy released when 6.0 g of water is condensed from water vapor is 13.53 kJ. Looking at the options, option B is the correct setup for the calculation.
Examples
Condensation is a crucial process in many natural phenomena, such as the formation of clouds and rain. Understanding the energy released during condensation helps us analyze weather patterns and climate change. For example, when water vapor in the atmosphere condenses to form clouds, it releases heat, which can influence local temperatures and weather conditions. This concept is also applied in industrial processes like distillation, where condensation is used to separate different components of a mixture based on their boiling points. Knowing the energy involved allows for efficient design and operation of such systems.
The energy released when 6.0 g of water is condensed from water vapor is approximately -13.53 kJ. The correct option for the setup of the calculation is B. The condensation process is the reverse of vaporization, and thus the energy released corresponds to the enthalpy of vaporization with a negative sign.
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