200809 NSERC Undergraduate Student Research Awards USRA

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• 2008-09 NSERC Undergraduate Student Research
  Awards (USRA)
• Department deadline is Friday, February 1, 2008
• In addition to the research experience, you will
  earn 4500.00 for 16 weeks at least 1,125.00
  from your professor.
• Students must have obtained a cumulative GPA of
  at least 8.0 or B- up to the time of application

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59-241 Labs

• Find your lab partner within the next few days.
• TAs will be in the classroom next Tuesday to sign
  you up and may also tell you which experiment you
  will start with
• Tutorial time is now posted on the website.

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Expressions of the equilibrium constant K

• The equilibrium constant, K, (a dimensionless
  quantity) can be expressed in terms of fugacities
  for gas phase reactions or activities for aqueous
  phase reactions.
• Fugacity ( a dimensionless quantity) is equal to
  the numerical value of partial pressure, i.e.
  pj/p? where p? 1 bar).
• The activity, a, is equal to the numerical value
  of the molality, i.e. bj/b? where b? 1 mol kg-1.

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For reactions occurring in electrolyte solutions

• Effects of the interactions of ions on the
  reaction process should be considered.
• Such a factor can be expressed with the activity
  coefficient, ?, which denotes distance from the
  ideal system where there is no ion-interaction.
• The activity shall now be calculated as aj
  ?jbj/b?
• For a reaction A B ? C D
• K

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The activities of solids are equal to 1

• a(solid) 1 (!!!)
• Illustration Express the equilibrium constant
  for the heterogeneous reaction
• NH4Cl(s) ? NH3(g) HCl(g)
• Solution
• In term of fugacity (i.e. partial
  pressure) Kp
• In term of molar fraction Kx

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Estimate reaction compositions at equilibrium

• Example 1 Given the standard Gibbs energy of
  reaction H2O(g) ? H2(g) 1/2O2(g) at 2000K is
  135.2 kJ mol-1, suppose that steam at 200k pa is
  passed through a furnace tube at that
  temperature. Calculate the mole fraction of O2
  present in the output gas stream.
• Solution (details will be discussed in class)
• lnK - (135.2 x 103 J
  mol-1)/(8.3145 JK-1mol-1 x 2000K)
• - 8.13037
• K 2.9446x10-4
• K
• Ptotal 200Kpa
• assuming the mole fraction of
  O2 equals x
• PO2 x Ptotal,
• PH2 2(xPtotal)
• PH2O Ptotal PO2 PH2
  (1-3x)Ptotal

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Equilibria in biological systems

• Biological standard state pH 7.
• For a reaction A vH(aq) ? P
• ?rG ?rG? RT
• ?rG? RT
• the first two terms of the above eq. form ?rG
• ?rG ?rG? 7vRTln10

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Example For a particular reaction of the form A
? B 2H in aqueous solution, it was found
that ?rG? 20kJ mol-1 at 28oC. Estimate the
value of ?rG.

• Solution ?rG ?rG? 7vRTln10
• here v - 2 !!!
• ?rG 20 kJ mol-1 7(-2)(8.3145x10-3 kJ
  K-1mol-1)
• x(273 28K)ln10
• 20 kJ mol-1 80.676 kJ mol-1
• -61 kJ mol-1
• (Note that when measured with the biological
  standard, the standard reaction Gibbs energy
  becomes negative!)

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Molecular Interpretation of equilibrium
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The response of equilibria to reaction conditions

• Equilibria respond to changes in pressure,
  temperature, and concentrations of reactants and
  products.
• The equilibrium constant is not affected by the
  presence of a catalyst.

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How equilibria respond to pressure

• Equilibrium constant K is a function of the
  standard reaction Gibbs energy, ?rG? .
• Standard reaction Gibbs energy ?rG? is defined at
  a single standard pressure and thus is
  independent of pressure.
• The equilibrium constant is therefore independent
  of pressure

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• K is independent of pressure does NOT mean that
  the equilibrium composition is independent of the
  pressure!!!
• consider the reaction 2A(g) ? B(g)
• assuming that the mole fraction of A
  equals xA at quilibrium, then xB 1.0 xA,
• K
• because K does not change, xA must
  change in response to any variation in Ptotal!!!

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Le Chateliers Principle

• A system at equilibrium, when subject to a
  disturbance, responds in a way that tends to
  minimize the effect of the disturbance.

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Example Predict the effect of an increase in
pressure on the Haber reaction, 3H2(g) N2(g)
? 2NH3(g).

• Solution
• According to Le Chateliers
  Principle, an increase in pressure will favor the
  product.
• prove K
• Therefore, to keep K unchanged, the
  equilibrium mole fractions Kx will change by a
  factor of 4 if doubling the pressure ptotal.

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The response of equilibria to temperature

• According to Le Chateliers Principle
• Exothermic reactions increased
  temperature favors the reactants.
• Endothermic reactions increased
  temperature favors the products.
• The vant Hoff equation
• (a)
  (7.23a)
• (b)
  (7.23b)

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Derivation of the vant Hoff equation

• Differentiate lnK with respect to temperature
• Using Gibbs-Helmholtz equation (eqn 3.53 8th
  edition)
• thus
• Because d(1/T)/dT -1/T2

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• For an exothermic reaction, ?rH? lt 0, thus
  , suggesting that increasing the
  reaction temperature will reduce the equilibrium
  constant.