None of the following cellular processes results in a net consumption of energy EXCEPT:
(a) Facilitated diffusion
(b) Osmosis
(c) Oxidation of glucose in eukaryotes
(d) Displacement of oxygen on hemoglobin by carbon monoxide in eukaryotes
(e) The removal of water by contractile vacuoles in Paramecium caudatum
This question may seem difficult at first glance, but let's use a combination of chemistry-, physics-, and biology-based knowledge to answer the question.
First of all, our biology courses teach us that diffusion along a concentration gradient is a spontaneous process that does not require energy (ATP in cells). Therefore, the answer is not (a). Also, we note that osmosis is a spontaneous process that results in net movement of water across a semi-permeable membrane. This occurs spontaneously, without any energetic input. This eliminates (b).
We next turn to chemistry-based reasoning. If you didn't recall that glucose is an energy source for eukaryotes, you should recall that the most oxidized form of carbon commonly found in biological systems is carbon dioxide. It is a molecule of high relative stability, and since we exhale it every second of the day, one must surmise glucose (sugar) is ultimately oxidized in our bodies to carbon dioxide, so this should yield much energy (which it does). This eliminates (c). In addition, hemoglobin is an iron-based globular protein, and oxygen binding occurs on the iron atom. Students of chemistry should recall that carbon monoxide is a much better ligand for iron (a Lewis acid) than oxygen (a poor ligand / Lewis base), thus displacement of oxygen by carbon monoxide should be energetically favorable (and thus (d) is eliminated).
This leaves (e). We may recall that Paramecium is a unicellular species that commonly lives in water. If we remember this, then using the information of choice (b) should tell us that water spontaneously enters Paramecium. This being said, it would take energy to reverse a spontaneous process (as physics teaches us that work, such as pumping water out of the Paramecium, requires energy). Thus, the correct answer is (e)!
A good video is shown here: http://www.youtube.com/watch?v=iG6Dd3COug4
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