The enthalpy of evaporation of water is 40.67 kJ/mol. Sunlight striking Earth's surface supplies 168 W per square meter (1 W = 1 watt = 1 J/s). (a) Assuming that evaporation of water is due only to energy input from the Sun, calculate how many grams of water could be evaporated from a 1.00 square meter patch of ocean over a 12-h day

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Convert the power supplied by sunlight from watts to joules over the 12-hour period. Use the formula: \( \text{Energy (J)} = \text{Power (W)} \times \text{Time (s)} \).

Calculate the total energy supplied by the Sun to the 1.00 square meter patch of ocean over 12 hours. Remember that 12 hours is equivalent to 43,200 seconds.

Determine the number of moles of water that can be evaporated using the total energy calculated and the enthalpy of evaporation. Use the formula: \( \text{Moles of water} = \frac{\text{Total energy (J)}}{\text{Enthalpy of evaporation (J/mol)}} \).

Convert the moles of water to grams using the molar mass of water (18.02 g/mol). Use the formula: \( \text{Mass (g)} = \text{Moles} \times \text{Molar mass (g/mol)} \).

Summarize the steps to find the total mass of water that can be evaporated from the given area over the specified time period.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Enthalpy of Evaporation

The enthalpy of evaporation, or heat of vaporization, is the amount of energy required to convert a unit mass of a liquid into vapor without a change in temperature. For water, this value is 40.67 kJ/mol, indicating that this amount of energy is needed to evaporate one mole of water. Understanding this concept is crucial for calculating how much water can be evaporated given a specific energy input.

Power and Energy Conversion

Power is the rate at which energy is transferred or converted, measured in watts (W), where 1 W equals 1 joule per second (J/s). In this context, sunlight provides energy at a rate of 168 W per square meter. To find the total energy available over a period, one must multiply the power by the time duration, converting hours into seconds for accurate calculations.

Mass-Energy Relationship

The mass-energy relationship in chemistry allows us to relate the energy absorbed during a phase change to the mass of the substance undergoing that change. By using the enthalpy of evaporation, we can determine how many grams of water can be evaporated by dividing the total energy available (calculated from power and time) by the energy required to evaporate a specific mass of water. This relationship is fundamental for solving the problem presented.

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The enthalpy of evaporation of water is 40.67 kJ/mol. Sunlight striking Earth's surface supplies 168 W per square meter (1 W = 1 watt = 1 J/s). (b) The specific heat capacity of liquid water is 4.184 J/g°C. If the initial surface temperature of a 1.00 square meter patch of ocean is 26 °C, what is its final temperature after being in sunlight for 12 h, assuming no phase changes and assuming that sunlight penetrates uniformly to depth of 10.0 cm?