In nature, CO2 is reacted with water during photosynthesis to make oxygen gas an

Question

In nature, CO2 is reacted with water during photosynthesis to make oxygen gas and formaldehyde in the following reaction: CO2(g) + H2O(g) —>O2(g) + CH2O(g)

?Hrxn= +244 kJ

MM CO2= 44.01 g/mol;

MM H2O= 18.02 g/mol;

MM O2= 32.00 g/mol;

MM CH2O= 30.03 g/mol

The energy required to drive this reaction comes from sunlight. If you assume that only 1% of the energy from sunlight is converted to heat, how many photons of 620nm light are required to react 1.000 g of CO2(g)? You may also assume that you have excess water.

Explanation / Answer

moles of CO2 = 1 g/44.01 g/mol = 0.023 moles

Energy from wavelength = 620 nm = 620 x 10^-9 m

Energy = hc/l

            = 6.626 x 10^-34 x 3 x 10^8/620 x 10^-9

            = 3.21 x 10^-19 J

1% of this is used = 3.21 x 10^-19 x 0.01 = 3.21 x 10^-21 J

For 1 g CO2 = 3.21 x 10^-21 J/0.023 moles = 1.40 x 10^-19 J/mol

dHrxn gives = +244 kJ = 244,000 J

So,

number of photons required = 244,000/1.40 x 10^-19 = 1.74 x 10^24

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