ESS 312 Geochemistry Lab # 2

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1 ESS 312 Geochemistry Lab # 2 You will have two lab periods to work on this assignment. It is due in lab one week after the second lab period. You may submit your assignment on paper or ed as single PDF file. Late assignment will not be accepted. Section AA: Due 4/19 Section AB: Due 4/19 Section AC: Due 4/20 Kimberlite is an unusual rock type that is famous as a source of diamonds. The diamonds are transported to the surface during eruption of the kimberlite. This means that kimberlite forms deep enough in the mantle (high pressure) where diamonds are stable. When the kimberlite erupts to the surface, it passes through the stability field of diamond. If we can calculate the conditions of diamond stability, we can draw some conclusions about how deep these eruptions started. In this problem set, we examine the reaction GRAPHITE DIAMOND, and use thermodynamic data to investigate the stabilities of these C polymorphs as functions of temperature and pressure. The following are some useful thermodynamic data from tables compiled by Robie and others (1978) published by the U.S. Geological Survey. PAY ATTENTION TO UNITS! You will need to use the following conversion factor: 1 cm 3 = 0.10 J/bar S o (298 K, 1 bar) J/mol-K Δ H o f, (298K, 1 bar) kj/mol Diamond Graphite CO O V (298K, 1 bar) (cm 3 /mol) *Cp (J/mol K) Diamond *T Graphite *T *These simplified heat capacity expressions are strictly only relevant to temperatures in the range 1000 K 1800 K, but we will use them here for the range 298 K 1300 K. 1

2 1. Because of the extreme pressures required to stabilize diamond, it is difficult to determine experimentally the ΔS and ΔH associated with the reaction GRAPHITE DIAMOND. However, we can extract these data from consideration of the following reactions at standard temperature and pressure (STP): I. Graphite + O 2 CO 2 II. Diamond + O 2 CO 2 A) What are the equations used to calculate the changes in enthalpy and entropy of a reaction? B) Using these equations, calculate the changes in enthalpy and entropy associated with reactions (I) and (II) above at 298 K and 1 bar. Show your work and include units. 2

3 C) Combine reactions (I) and (II) to obtain the ΔS and ΔH for the final reaction: III. Graphite Diamond Remember, when you reverse a reaction, you change the sign of your ΔS and ΔH, but the magnitude remains the same. Show your work for combing the reactions. D) What formula, using enthalpy and entropy, is used to calculate the Gibbs free energy of a reaction at STP. What does the value (negative, positive, or zero) of the Gibbs free energy tell you about your reaction? E) Using the above data and the formula from question 1D to calculate ΔG for reaction (III) at 298K, 1 bar, and indicate which polymorph is stable under these conditions. Verify your answer using what you know about the relative stability of the two polymorphs. 3

4 2. Now that we have considered this reaction at STP, let s consider this reaction at temperatures and pressures more realistic for the mantle. A) Write the general equation that describes the free energy change of a reaction at any temperature, T, and at the reference pressure, P r, of 1 bar (i.e., at T = any T, and P = P r ). ΔG graphite diamond (T, P r ) = B) Use the equation from Question 2A and the results from Question 1 to calculate the free energy change of the Graphite Diamond reaction at 1300K and 1 bar. What is the stable polymorph at these conditions? Pay attention to your units! Show your work on Pages 4 and 5 (left intentionally blank) 4

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6 C) You can also calculate the Gibbs free energy at non-standard pressures. Write the equation to calculate the free energy change for any reaction at any temperature and pressure (i.e., at any T and P) Hint: you only need to add one additional term to the equation you wrote in Question 2A. ΔG graphite diamond (T, P) = D) Use this equation to calculate the pressure required for diamond and graphite to coexist at equilibrium at 1300K. For this calculation, assume that the coefficients of thermal expansion and isothermal compressibility are both equal to zero. Hint: think about the value of Gibbs free energy at equilibrium: ΔG graphite diamond in equil (1300, P) = Use the Clapeyron equation to calculate the slope of the graphite-diamond equilibrium curve in P-T space. Plot this curve and predict which polymorph is stable at 3.5 GPa and 1100K. Do not hand draw figure and make sure you figure is properly labeled. 6

7 4. Diamonds are erupted in explosive volcanic rocks called kimberlites. A group of kimberlites in South Africa has a characteristic mineralogy and type of diamond that sets it apart from other diamond occurrences. These kimberlites are only found on continental crust that is Archean in age. None of these types of kimberlites is found in adjoining but younger crust. Minerals in the kimberlite rock allow us to determine that the eruption occurred about 90 million years ago (Ma). There are also mineral inclusions within these diamonds that allow us to determine the age of the diamonds themselves. They did not form 90 Ma during eruption of the kimberlite, but formed 3.3 to 3.5 billion years ago (Ga). We also know that the kimberlitic magma formed at a temperature of C from a source that has a mineralogy similar to garnet-bearing mantle peridotite. What do your results imply about the origin of these diamonds, and the structure and development of the oldest (Archean) continents preserved on Earth? 7

Solubility, mixtures, non-ideality OUTLINE

Solubility, mixtures, non-ideality Equilibrium? OUTLINE Class exercise next class bring laptop, or use class tablet Enthalpy, Entropy The Gibbs Function ΔG and K Mixtures Chemical Potential 1 Enthalpy