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Gibb's Phase Rule

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I have a problem understanding the degrees of freedom for two binary diagrams because they have different degrees of freedoms in some parts of the diagram and I don't get why they have that. It would be great if you could explain if this is because of less chemical potential equilibrium or from less variables from the derivation of degrees of freedom that I have attached in the question. It is taken from Atkins physical chemistry. Question is attached.

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Solution Summary

Clarifying specific applications of Gibb's phase rule.

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  • "Thankyou for the feedback. I have a few question though; With the first statistic about cost below... “According to Sigma-Aldrich catalog, cost of 1L octane is AUD $ 392.00, whereas the cost of 1L ethanol is AUD $196.00. Moreover, if ethanol is obtained from sugar industry as a by-product, it may cost even less. Source of oxygen is ambient atmosphere, so it costs nothing. So ethanol is much cheaper than petrol, in fact it is half-priced: AUD $ (392-196) = $ 196.” I didn't think it made sense because the cost of petrol per litre is normally a dollar something or even less than a dollar not a couple of hundred of dollars. For example, a statistic that I found in america was: "U.S. ethanol production costs are about $1.20 per gallon of ethanol, or $1.82 per gallon on a gasoline-equivalent basis." However, I was wondering whether you could find an Australian statistic. Also, you mentioned that H20 is not a greenhouse gas. However, in the combustion equations it is actually carbon dioxide and water vapour which are produced and they are both greenhouse gases. Finally, how do I calculate the energy efficiency of ethanol and petrol? "
  • "Thank you!"
  • "Didnt really answer my questions but gave me a start at least."
  • "Once again this is tremendous help I can't thank you enough for not only working the problem but explaining in detail how and why!! KR"
  • "Awesome thank you so much for the help!!!"
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