Sucrose (C12H22O11) is produced by plants as follows: 12 CO2(g) + 11 H2O(l) → C12H22O11 + 12 O2(g) H = 5645 kJ About 4.8 g of sucrose is produced per day per square meter of the earth's surface. The energy for this endothermic reaction is supplied by the sunlight. About 0.1 % of the sunlight that reaches the earth is used to produce sucrose. Calculate the total energy the sun supplies for each square meter of surface area. Give your answer in kilowatts per square meter 1kW/m2 where 1W = 1 J/s2.

Verified step by step guidance

1. Determine the moles of sucrose produced per day per square meter by using the molar mass of sucrose (C_{12}H_{22}O_{11}).
2. Calculate the energy required to produce the given moles of sucrose using the enthalpy change (\( \Delta H = 5645 \text{ kJ} \)) for the reaction.
3. Since only 0.1% of the sunlight is used to produce sucrose, calculate the total energy supplied by the sun by dividing the energy required by 0.001.
4. Convert the total energy from kilojoules to joules (1 kJ = 1000 J).
5. Convert the energy from joules per day to watts per square meter by dividing by the number of seconds in a day (86400 seconds).

Key Concepts

Photosynthesis

Photosynthesis is the biochemical process by which green plants, algae, and some bacteria convert light energy into chemical energy, specifically glucose, using carbon dioxide and water. The overall reaction involves the absorption of sunlight, which drives the endothermic reaction that produces glucose (or sucrose) and oxygen. Understanding this process is crucial for calculating the energy involved in sucrose production.

Energy Conversion

Energy conversion refers to the transformation of energy from one form to another. In the context of photosynthesis, solar energy is converted into chemical energy stored in sucrose. This concept is essential for determining how much solar energy is required to produce a specific amount of sucrose, as it involves understanding the relationship between energy input and output in chemical reactions.

Kilowatt and Energy Calculation

A kilowatt (kW) is a unit of power equivalent to 1,000 watts, where 1 watt is defined as 1 joule per second. To calculate the total energy supplied by the sun per square meter, one must convert the energy produced in kilojoules to kilowatts, taking into account the time frame over which the energy is produced. This conversion is vital for expressing energy in a standardized unit that reflects power output over time.