## Hydrogen Evolution

(a) calculate the molar enthalpy (relative to the initial pure components) for both cases. The specific heats of sulfuric acid and water are 147.7 and 75.4 J/mole-K, respectively. Assume ideality only for the purpose of calculating the specific heat of the mixture. The density of sulfuric acid is 1.84 g/cm3.

(b) plot the data according to the method treated in problem 7.26 and determine the partial molar quantities. At low acid concentrations, the partial molar volumes of sulfuric acid and water in their solutions are reported to be 45 and 17.5 cm3/mole, respectively. How does this compare to your result

(c) Assume that this mixture obeys regular solution theory and determine the interaction parameter Q.

(i) are the two experiments consistent in the sense that they give the same interaction parameters?

(ii) Is the sign of Q physically reasonable?

(d) The plot below shows the partial molar enthalpies for the sulfuric acid/water system. From this graph, calculate the excess enthalpy of the solutions used in the class demonstration and compare the results with the values of hex obtained in part (b)

(e) How would the temperature increase differ if mixing were performed as follows:

(i) Water is added to the acid

(ii) Acid is added to the water

(iii) Acid and water are mixed in proportions equal to their mole fractions in the final solution (i.e., the composition is kept constant as the solution is created)

(f) In order to dispose of the acid solutions remaining from the demonstration, they must first be neutralized with a base such as NaOH.

(i) write the neutralization reaction

(ii)Calculate the mass of NaOH needed to neutralize the acid from the tests 7.3 Complete the following proofs:

7.4 The following formula has been proposed for the excess enthalpy of mixing of nonideal solutions that do not obey regular solution theory:

h= CRTx 2AxB

(a) What are the expressions for the activity coefficients of A and B?

(b) Do the activity coefficients obey the Gibbs-Duhem relation?

(c) Do the activity coefficients approach physically acceptable limits as xA approaches zero and xA approaches unity?

7.5 Calculate the enthalpy and entropy changes when one mole of solid Cr at 1873 K is added to a large quantity of a liquid Fe-Cr alloy (xFe = 0.78) at the same temperature. "Large" means that the composition and solution properties are only slightly changed by addition of the mole of Cr; a Taylor series expansion relating the entropy of mixing of the final composition to that of the initial composition eliminates the need to quantify "large". Assume that the heat capacity difference between solid and liquid Cr is negligible. The heat of fusion of Cr is 21 kJ/mole and its melting point is 2173 K. Assume that Fe-Cr solutions are ideal.

Hint: the Taylor series expansion of the function f(x) around x = 0 is: f(x) = f(0) + (df/dx)x=o (x - 0) +

7.6 Repeat problem 7.5 with the following changes:

- The Cr is initially liquid (rather than solid) at 1873 K

- The solution is regular rather than ideal, and the activity coefficient of Cr in the liquid alloy is 0.5.

How much heat given off or absorbed during the mixing process?

Hint: To determine the enthalpy change, first show that AH = hCr - hCr then use

Eq (7.23) to relate this difference to the activity coefficient.

7.7 What is wrong with the following equation for the activity coefficient of component A in an A-B solution? ln y A = CxAxB (discuss all potential answers):

(a) The activity coefficient it predicts is less than unity.

(b) It does not obey the Gibbs-Duhem equation

(c) yA has the wrong limit as xA approaches zero

(d) yA has the wrong limit as xA approaches unity

7.8 Prove that the activity coefficients from regular solution theory obey the Gibbs-Duhem equation.

7.9 The activity coefficient of component B in an A-B solution at a fixed temperature is represented by: ln = CxA - DxA . What is the corresponding equation for lnyA?

7.10 The generic partial molar quantity yi (e.g hi, gi, vi, etc) is defined by the following relationship to the total solution property Y:

where n, is the number of moles of component i. From these equations prove that: 