## Monday, December 28, 2015

### Standard Gibbs vs Helmholtz Free Energy Change: An Apparent Paradox

Consider the following equilibrium
$$\text{A} + \text{B} \rightleftharpoons \text{AB}$$
and the following three experiments performed at the same temperature.

Experiment 1: To an empty, rigid container with volume $V_1$ is added $p_{\text{A},0}$ of molecule $\text{A}$ and $p_{\text{B},0}$ of molecule $\text{B}$.  The system is allowed to go to equilibrium, $p_{\text{AB},1}$ is measured, and $K_1$ is computed as
$$K_{p,1}=K_1=\frac{p_{\text{AB},1}p^\circ}{p_{\text{A},1}p_{\text{B},1}}$$
where $p_{\text{A},1} = p_{\text{A},0}-p_{\text{AB},1}$

Since the experiment is carried out at constant volume, equilibrium is defined as $dA = 0$ so the standard free energy change computed from $K_1$ should correspond to a standard Helmholtz free energy change, $\Delta A^\circ_1$.

Experiment 2: A balloon is filled with $p_{\text{A},0}$ of molecule $\text{A}$ and $p_{\text{B},0}$ of molecule $\text{B}$. After equilibrium the volume of the balloon is $V_2$ and $p_{\text{AB},2}$ is measured and $K_2$ computed.

Since the experiment is carried out at constant pressure, equilibrium is defined as $dG = 0$ so the standard free energy change computed from $K_2$ should correspond to a standard Gibbs free energy change, $\Delta G^\circ_2$.

Experiment 3: Experiment 1 is repeated using a rigid container with volume $V_2$.

$K$ does not depend on the volume, so $K_3 = K_1$ and $\Delta A^\circ_3=\Delta A^\circ_1$. However, since the temperature and final volume is the same as in Experiment 2, the internal pressure and hence the partial pressures must be the same.  Thus $K_3 = K_2$ and $\Delta A^\circ_3=\Delta G^\circ_2$.  It follows that
$$\Delta A^\circ_1=\Delta G^\circ_2$$

So there is really only one standard free energy change associated with Eq 1, but is it $\Delta G^\circ$ or $\Delta A^\circ$?

The change in standard Helmholz free energy is not the same as the change in standard chemical potential
The equilibrium constant is related to the change in standard chemical potential
$$K = e^{-\Delta \mu^\circ RT}$$
The chemical potential is defined as
$$\mu _X = {\left( {\frac{{\partial G}}{{\partial {n_X}}}} \right)_{p,T,n'}} = {\left( {\frac{{\partial A}}{{\partial {n_X}}}} \right)_{V,T,n'}}$$
For a one-component system, $G = nG_m$, and the chemical potential is simply the molar Gibbs energy of the substance because
$$\mu = {\left( {\frac{{\partial G}}{{\partial {n_X}}}} \right)_{p,T,n'}} = {\left( {\frac{{\partial nG_m^{}}}{{\partial {n_X}}}} \right)_{p,T,n'}} = G_m$$
so we can write
$$K = e^{-\Delta G^\circ RT}$$
where
$$\Delta G^\circ = G^\circ_m(\text{AB)} -G^\circ_m(\text{A)} -G^\circ_m(\text{B)}$$
However, the chemical potential is not equal to the molar Helmholtz free energy
$$A_m = {\left( {\frac{{\partial A}}{{\partial {n_X}}}} \right)_{p,T,n'}} \ne {\left( {\frac{{\partial A}}{{\partial {n_X}}}} \right)_{V,T,n'}}$$
Notice that the middle term is for constant $p$ and the last term is for constant $V$.  So I can't write the equilibrium constant using $\Delta A^\circ$ computed partial molar standard Helmholtz free energies
$$K = {e^{ - \Delta {\mu ^{\circ}}/RT}} \ne {e^{ - \Delta {A^{\circ}}/RT}}$$
Here's why.  The Helmholtz free energy can be written in terms of the partition function $Q=q^N/N!$
$$A = -nRT\ln \left( {\frac{{eq}}{{n{N_A}}}} \right) = -nRT\ln \left( {\frac{{eq_0V}}{{n{N_A}}}} \right)$$
The chemical potential is
$$\mu _X = {\left( {\frac{{\partial A}}{{\partial {n_X}}}} \right)_{V,T,n'}} = - RT\ln \left( {\frac{q}{{n{N_A}}}} \right)$$
To get the partial molar Helmholtz free energy we need to keep $p$ constant, so we substitute $V=nRT/p$ before differentiating, which cancels out the $n$ in the parenthesis
$$A_m = -RT\ln \left( {\frac{{e{q_0}RT}}{{{N_A}p}}} \right) = - RT\ln \left(\frac{eq}{N_A} \right)$$
So from this we can see that
$$\mu_X = A_m + RT$$
In the case of $G$
$$G = A + RT =-nRT\ln \left( {\frac{{q}}{{n{N_A}}}} \right)$$
and we make the substitution $V=nRT/p$ before differentiating to find $\mu$
$$\mu = - RT\ln \left(\frac{q}{N_A} \right) = G_m = A_m + RT$$
So measuring the equilibrium constant for the reaction in Eq 1 gives us
$$\Delta \mu^\circ = \Delta G^\circ = \Delta A^\circ - RT$$ ## Tuesday, December 15, 2015

### My Vision for ACS Omega

Update: ACS Omega is too expensive

A few weeks ago I was invited to submit my application (a vision statement and a CV) for a co-editor-in-chief position at ACS Omega.  Here's my vision statement.  I have made one change: at the time I didn't know the final name of the journal and used a working title instead.  The application is still pending.

My Vision for ACS Omega
Jan H. Jensen
University of Copenhagen

Open Access and Open Science: Leading by Example
Since 2012 I have published the bulk of my papers in PLoS ONE and PeerJ - one of the few chemists to do so. My switch to OA was catalyzed mainly by the Research Work Act  - legislation that sought to “prohibit open-access mandates for federally funded research and effectively revert the US NIH Public Access Policy, which requires taxpayer-funded research to be freely accessible online” (1). The RWA was clearly a result of lobbying efforts by commercial publishers and, in my opinion, designed to maximize profits at the expense of servicing science. This got me to try and, ultimately, embrace OA (2) and open science.

I have found the lack of “perceived importance” and “scope” as editorial criteria at PLoS ONE and PeerJ incredibly liberating: they allow me to be more innovative (i.e. take more chances) in my research and makes the papers easier to write. Equally liberating is the fact that my work can be used by me or anyone else without restrictions under the CC-BY licence, which for me and most other open access activists is synonymous with OA.

I deposit all my manuscripts on arXiv or PeerJ Preprints prior to submission. I sign all my manuscript reviews, I post my reviews on Publons.com (3), and I publish all the reviews I receive, either on PeerJ (4) or on my blog (5). Furthermore I founded Computational Chemistry Highlights (6) in 2012 that openly reviews important recent papers in computational and theoretical chemistry. I actively campaign for these practices on Twitter and I write extensively about open access and open science on my blog (7). As co-editor-in-chief of ACS Omega I would have the track record needed to be an effective advocate of OA for chemistry.

ACS Omega: The Journal of First Choice
ACS Omega has the potential to become the largest chemistry journal in the world and this will be my goal as co-editor-in-chief. Obviously, a lot of papers that are rejected by other ACS journal because of scope and lack of perceived importance should be funneled to ACS Omega. However, my vision for ACS Omega is as a journal of first choice due to its purely objective review criteria that welcomes innovative ideas and frank discussions of the merits and weaknesses of the results.

In fact I propose that a self-critical discussion of possible limitations of the study is a mandatory part of an ACS Omega paper, with the understanding that it will not hurt the chances of acceptance. This is how science is supposed to work: as a scientist you are supposed to be your own worst critic, but you wouldn’t know it from reading the current literature. I would like ACS Omega to be open to all types of papers in addition to conventional research articles including insights/perspectives, software notes, and replication studies. In my view science advances incrementally and benefits from input at every stage: one should publish early and publish often. I would also like to implement eLife’s Research Advances, “a short article that allows the authors of an eLife paper to publish new results that build on their original research paper” in some way (8).

ACS Omega: The Most Affordable OA (CC-BY)  Option
If one removes the “perceived importance” and “scope” criteria from the editorial decision process then the only meaningful criteria for where to publish is the price. This is the reason I switched from PLoS ONE to PeerJ. Obviously I cannot be a co-editor-in-chief of a journal where I will not publish myself. ACS Omega must therefore offer an APC of $500 or less (or a PeerJ-style APC model) for CC-BY for me to interested in the position. I currently pay an average of$300/paper to publish CC-BY in PeerJ, so $500 is already a compromise for me. With ACS Omega ACS has a unique chance to fulfill its mission to “advance the broader chemistry enterprise and its practitioners for the benefit of Earth and its people” by making the APC for CC-BY$0. Think of ACS Omega as part of the ACS’s other activities such as education, outreach, and awards and not as a means of generating funds for such activities. I strongly urge the ACS to consider this option and will happily do the job for free should the ACS choose to do so.

To keep the APC as low as possible I suggest several cost-saving measures:
• Typesetting is optional and costs extra for the author. Your CV says “Peer Reviewed Publications”, not “Typeset Publications” and I predict many chemists would gladly do their own formatting (perhaps given suitable template) if they can save $500/paper. Other disciplines are catching onto this (9,10) and ACS Omega might as well be on the forefront in chemistry. • A smaller editorial board relative to journal volume. I predict that ACS Omega editors will be able to handle more submissions compared to other ACS journals due to ACS Omega’s more objective editorial criteria and more open review process (see below). • Less travel/more on-line communication. Communication within other ACS journals are still based on the premise that most editors reside within the US and would go to ACS meetings anyway. We need to do things differently at ACS Omega for purely practical reasons, but this will also lower costs. • I would also like to investigate the possibility of corporate sponsorship of the journal to see if it can be done in an ethical way and without conflict of interest issues. ACS Omega: A Truly Open Journal I strongly believe that openly sharing preprints prior to submission greatly benefits science. As co-editor-in-chief I will publicly encourage authors to deposit preprints prior to submission to ACS Omega. Furthermore, I will work with arXiv on establishing a chemistry section and encourage the ACS to support arXiv. The current running costs of arXiv is$826,000. I think the ACS should contribute 10-15% of the running costs if arXiv establishes a chemistry section. Alternatively, the ACS should start their own preprint server.

I am a strong believer in open peer review. I suggest that ACS Omega follows the PeerJ model where the reviewers choose whether to remain anonymous, while the authors choose whether to publish the reviews. If the authors choose to publish the reviews there should be an option to append it to the manuscript when downloading the pdf. I realize that implementing such a feature increases the cost of the journal, so alternatively the journal should encourage reviewers to post their reviews on Publons.com.  Related to this I suggest that editor’s names be openly associated with individual papers.

I am a strong believer in open post publication peer review and I would like to see a comment section for each ACS Omega paper. I realize that implementing such a feature increases the cost of the journal, so alternatively the journal should encourage reviewers to post their comments on PubPeer. Similarly, I suggest a partnership with Altmeric.com to keep track of PubPeer discussions, Tweets and blogposts on individual papers.

I am a strong believer in open data and code. ACS Omega should strongly encourage this practice and make it an explicit part of the editorial decision (11) for several reasons: Often the data turns out to be the most important contribution (e.g. data for benchmarking or modeling), it is crucial for informed pre- and post-publication peer reviews, and it helps ensure reproducibility. I am very happy to see that ACS already has partnered with Figshare.

ACS Omega: Transforming the Field of Chemistry
Chemistry is in my opinion the least open of the natural sciences and that as result the field is not progressing as fast as it could. Most chemistry papers are not accessible to the taxpayers who paid for the work (12). The ideas and data within these papers remain inaccessible for other researchers for months or years until “the data tells a story”, “there’s enough for a JACS paper”, or while the manuscript is makes its way down the “impact ladder”. The criterion that something has to be demonstrably “first” to be published means that ideas and data are jealously guarded and most conference talks are used to rehash published results and ideas rather than to get feedback on or develop new ideas. The ACS shares a large part of the blame for this state of affairs as it tends to “set the tone” within our community. For example, all ACS journals have “importance” as a criteria, and aggressively promote an impact factor-based journal hierarchy. Many ACS journals forbid preprint depositions and the ones that allow it do not state so explicitly, leading to a “better not to, be on the safe side” attitude among most chemists.

However, with ACS Omega, the ACS has the unique opportunity to almost single handedly change all this and, ultimately, increase the pace of discovery and genuine innovation in chemistry. As PLoS ONE has shown for the bio/medical community, this is done by actively and explicitly encouraging openness on all fronts - both in the journal policies and by the people who lead it.  I would be honored to be part of this transformation as co-editor-in-chief and would work tirelessly to make it happen.

References 