Textbook Question
What is the molarity of Na+ in a solution of NaCl whose salinity is 5.6 if the solution has a density of 1.03 g>mL?
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Ch.18 - Chemistry of the Environment
Chapter 18, Problem 39b
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?
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Calculate the total energy supplied by sunlight over 12 hours. Use the formula: \( \text{Energy} = \text{Power} \times \text{Time} \). Convert 12 hours into seconds and multiply by the power per square meter (168 W/m²) to find the total energy in joules.
Determine the mass of the water being heated. Use the volume of water (1.00 m² area and 10.0 cm depth) to find the volume in cubic meters, then convert to liters (1 m³ = 1000 L). Since the density of water is approximately 1 g/mL, the mass in grams is numerically equal to the volume in milliliters.
Use the specific heat capacity formula to find the change in temperature: \( q = m \cdot c \cdot \Delta T \), where \( q \) is the energy calculated in step 1, \( m \) is the mass of the water, \( c \) is the specific heat capacity (4.184 J/g°C), and \( \Delta T \) is the change in temperature.
Rearrange the specific heat capacity formula to solve for the change in temperature: \( \Delta T = \frac{q}{m \cdot c} \). Substitute the values for \( q \), \( m \), and \( c \) to find \( \Delta T \).
Add the change in temperature \( \Delta T \) to the initial temperature (26 °C) to find the final temperature of the water after 12 hours of sunlight exposure.
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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 significant energy is needed to change water from liquid to gas. This concept is crucial for understanding energy transfer in processes involving water, especially in the context of temperature changes and phase transitions.
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Specific Heat Capacity
Specific heat capacity is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius. For liquid water, this value is 4.184 J/g°C, which means it can absorb a considerable amount of heat before its temperature changes significantly. This property is essential for calculating temperature changes in water when exposed to heat sources, such as sunlight.
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Energy Transfer from Sunlight
Energy transfer from sunlight can be quantified in terms of power, measured in watts (W), where 1 W equals 1 joule per second. In this scenario, sunlight provides 168 W/m², meaning that each square meter receives 168 joules of energy every second. Understanding this concept is vital for calculating the total energy absorbed by a given area over time, which directly influences the temperature change of the water.
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Related Practice
Textbook Question
Phosphorus is present in seawater to the extent of 0.07 ppm by mass. Assuming that the phosphorus is present as dihydrogenphosphate, H2PO4-, calculate the correspond-ing molar concentration of H2PO4- in seawater.
Textbook Question
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
Textbook Question
The enthalpy of fusion of water is 6.01 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 ice is 2.032 J/g°C. If the initial temperature of a 1.00 square emter patch of ice is -5.0°C, what is its final temperature after being in sunlight for 12 h, assuming no phase changes and assuming that sunlight penetration uniformly to a depth of 1.00 cm?
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