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The sun supplies energy at a rate of about 1.0 kilowatt per square meter of surface area (1 watt = 1 J/s). The plants in an agricultural field produce the equivalent of 20. kg sucrose (C 12 H 22 O 1l ) per hour per hectare (1 ha = 10.000 m 2 ). Assuming that sucrose is produced by the reaction 12 CO 2 ( g ) + 11 H 2 O ( l ) → C 12 H 22 O 11 ( s ) + 12 O 2 ( g ) Δ H = 5640 KJ calculate the percentage of sunlight used to produce the sucrose—that is, determine the efficiency of photosynthesis.

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Chemistry

10th Edition
Steven S. Zumdahl + 2 others
Publisher: Cengage Learning
ISBN: 9781305957404

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Chemistry

10th Edition
Steven S. Zumdahl + 2 others
Publisher: Cengage Learning
ISBN: 9781305957404
Chapter 6, Problem 132CP
Textbook Problem
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The sun supplies energy at a rate of about 1.0 kilowatt per square meter of surface area (1 watt = 1 J/s). The plants in an agricultural field produce the equivalent of 20. kg sucrose (C12H22O1l) per hour per hectare (1 ha = 10.000 m2). Assuming that sucrose is produced by the reaction

12 CO 2 ( g ) + 11 H 2 O ( l ) → C 12 H 22 O 11 ( s ) + 12 O 2 ( g )     Δ H = 5640   KJ

calculate the percentage of sunlight used to produce the sucrose—that is, determine the efficiency of photosynthesis.

Interpretation Introduction

Interpretation: The efficiency of photosynthesis process should be determined.

Standard enthalpy of formation:

  • The change in enthalpy that associate with the formation of one mole of a product from its pure elements, with all substances in its standard states is called as a standard enthalpy of formation.
  • The energy change of a reaction is related to the enthalpy change.

Explanation of Solution

Explanation

Sun furnished energy is 1.0 kW/m2

             Produced sucrose is 20 kg

             Enthalpy change is 5640 kJ

             Agricultural field area is 10.000 m2

To calculate the energy required for 20 kg of sucrose production.

Photosynthesis reaction is,

                         12CO2(g)+11H2O(l)→C12H22O11(s)+12O2(g)

Sucrose molecular weight is 342.3 g

= Mass of sucrose produceh×1 ​mol of sucrosesucrose molecular weight×enthalpy changy1 mol=20,000g1h×1342.3 g×5640 KJ1 mol=3.3×105 KJh 

  • The enthalpy change for per mole of sucrose production is multiplied by the mole of 20 kg sucrose to get energy required for 20 kg of sucrose production.
  • The given enthalpy change and molecular weight of sucrose are plugging in the above equation to get the energy required for 20 kg of sucrose production.
  • The energy required for 20 kg of sucrose production is 3.3×105 KJh  .

To calculate the furnished sun energy for per hour.

             Furnished sun energy= 1.0kWm2                              1

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