Molar flux through membrane - Chemistry Stack Exchange most recent 30 from chemistry.stackexchange.com 2019-08-20T16:21:36Z https://chemistry.stackexchange.com/feeds/question/114592 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://chemistry.stackexchange.com/q/114592 1 Molar flux through membrane lotte07 https://chemistry.stackexchange.com/users/77294 2019-04-30T09:16:55Z 2019-04-30T10:19:49Z <blockquote> <p>Consider a liquid of pure <span class="math-container">$\ce{A}$</span> covered by a composite membrane through which the vapor of <span class="math-container">$\ce{A}$</span> is diffusing. The membrane consists of two layers of thickness <span class="math-container">$l_1$</span> and <span class="math-container">$l_2$</span>. The diffusion coefficient of <span class="math-container">$\ce{A}$</span> in the two layers are <span class="math-container">$D_{\ce{A},1}$</span> and <span class="math-container">$D_{\ce{A},2}$</span> respectively. On the lower side of the membrane, the concentration of <span class="math-container">$\ce{A}$</span> (<span class="math-container">$c^s_\ce{A})$</span> is controlled by the vapor pressure of <span class="math-container">$\ce{A}$</span>. On the upper side the concentration of <span class="math-container">$\ce{A}$</span> is zero. The solubulity of <span class="math-container">$\ce{A}$</span> in the two membrane layers is the same.</p> <p>(a) Derive the expression for the flux <span class="math-container">$J_\ce{A}$</span> through the composite membrane</p> <p><a href="https://i.stack.imgur.com/9G1yw.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/9G1yw.png" alt="enter image description here"></a></p> </blockquote> <p>The flux through a membrane is given by the equation:</p> <p><span class="math-container">$$J_\ce{A} = \frac{D_{AB}}{L}\left(c^{(m)}_{\ce{A},F} - c^{(m)}_{\ce{A},P}\right)$$</span></p> <p>where, <span class="math-container">$c^{(m)}_{\ce{A},F}$</span> and <span class="math-container">$c^{(m)}_{\ce{A},P}$</span> are the concentrations at the edges inside the membrane.</p> <p>So I would assume that <span class="math-container">$c^{(m)}_{\ce{A},F}$</span> = <span class="math-container">$c^s_\ce{A}$</span> and <span class="math-container">$c^{(m)}_{\ce{A},P}$</span> = <span class="math-container">$c_\ce{A}$</span></p> <p>and because there are two membranes I would have to combine the diffusion coefficients as well as the lengths, which I do by addition to get the equation:</p> <p><span class="math-container">$$J_\ce{A} = \frac{D_{\ce{A},1} +D_{\ce{A},2}}{l_1 +l_2} (c^s_\ce{A} - c_\ce{A})$$</span></p> <p>I am unsure if this is the correct way of deriving the expression for the flux when there are two membranes. Am I thinking correct?</p> <p><strong>Edit</strong></p> <p>I named the third concentration in the membrane <span class="math-container">$c_m$</span>. Then I made two equations for the molar flux.</p> <p><span class="math-container">$$J_\ce{A} = \frac{D_{A,1}}{l_1}(c^s_A - c_m)$$</span></p> <p><span class="math-container">$$J_\ce{A} = \frac{D_{A,2}}{l_2}(c_m - c_A)$$</span></p> <p>When rearranging and solving for <span class="math-container">$J_A$</span>, I get:</p> <p><span class="math-container">$$J_\ce{A} = \frac{(c^s_A - c_A)}{\frac{l_1}{D_{A,1}}+\frac{l_2}{D_{A,2}}}$$</span></p> <p>But that is the same answer as I got before</p>