Oxygen diffuses from the surface of insects to the interior th...

Question

Oxygen diffuses from the surface of insects to the interior through tiny tubes called tracheae. An average trachea is about 2 mm long and has cross-sectional area of 2 x 10^-9 m². Assume the concentration of oxygen inside is half what it is outside in the atmosphere. Calculate the diffusion rate J. Assume the diffusion constant is 1 x 10^-5 m²/s.

Accepted Answer

Hi, everyone. Let's take a look at this practice problem dealing with diffusion. This problem says a typical stoma on a plant leaf is about 30 micrometers long and has a cross sectional area of 3.0 multiplied by 10 to the negative 9 m squared. Carbon dioxide exits cells of the leaf through these tiny openings. Assume that the concentration of carbon dioxide inside the leaf is twice that of the outside atmosphere where the concentration of CO2 is approximately 0.017 moles per meter cubed given the diffusion cost of 2.0 multiplied by 10 to the negative 5 m squared per second. Calculate the diffusion rate. J we're given four possible choices as our answers. For choice A we have 1.7 multiplied by 10 to the negative 11 moles per second. For choice B, we have 3.4 multiplied by 10 to the negative 11 moles per second. For choice C we have 5.1 multiplied by 10 to the negative 11 moles per second. And for choice D, we have 6.8 multiplied by 10 to the nega negative 11 moles per second. Now the question asks us to calculate our diffusion rate. J. So recall your formula for the diffusion rate that is J is equal to D multiplied by a multiplied by delta C divided by L where J here is our diffusion rate. D is our diffusion constant. A is the cross sectional area. Delta C is our difference in concentration between the two ends and L is going to be our length. Now, we're given all the information in the problem except for our delta C. However, we were given information about one of the concentrations, the concentrations on the outside of the leaf. So we can actually use that along with the relationship between the concentrations on the outside and the inside to calculate our delta C. So our delta C here is just gonna be the difference in the concentrations from the outside and the inside. So we'll have delta C is equal to C one minus C two, where C one is gonna be the concentration on the inside of the leaf. And C two will be the concentration outside the leaf. Now, we're told in the problem that the concentration inside the leaf is twice that of the concentration of CO2 on the outside. So that means that C one is equal to two multiplied by C two. So we can plug that relationship into our formula for delta C, we'll have delta C is equal to two multiplied by C two minus C two. That means that delta C is equal to C two. However, we were given the concentration outside the leaf in the problem. And so that means that our delta C is going to be equal to the 0.017 moles per meter cubed. So now we have all the information that we need to calculate our diffusion rate. So coming back to the diffusion rate, we'll have J is equal to, for our diffusion constant, We were given that in the problem that is the two multiplied by 10 to the negative five meters squared per second. And that gets multiplied by our cross sectional area which we are also given in the problem that is the three multiplied by 10 to the negative 9 m squared. And that gets multiplied by delta C that we just calculated which is the 0.017 moles per meter cubed that gets divided by the length of our stoma which we again the problem s 30 micrometers. However, I'm going to need that in meters. So I need to convert that into meters. So I will get 30 multiplied by 10 to the negative six meters. So recall that to convert from micrometers to meters, you need to multiply the value by 10 to the negative six. So now that I have values on the right hand side, I can just plug this into my calculator and I'll get J is equal to 3.4 multiplied by 10 to the negative 11 moles per second. That's the answer that I'm looking for. And if I compare that to my answer choices, this corresponds to answer choice B. So the trick to this problem was just to use our formula for the diffusion rate J. However, in order to use this um equation, we need to actually calculate our delta C based on the information that we're given. So we're actually given only one of the concentrations. But we were given a relationship between that concentration, which was the concentration of CO2 outside the leaf along with the relationship between that and the concentration of CO2 inside the leaf. And so once we use that relationship, we could calculate a value for our delta C which we could then plug in along with the other values that we're given the problem into our formula for J and to calculate our diffusion rate. So I hope that this has been useful and I'll see you in the next video.

Key Concepts

Diffusion

Fick's Law of Diffusion

Concentration Gradient

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