(a) The volume of an aqueous solution of NaCl at 25 degree C was measured at ser
ID: 500669 • Letter: #
Question
(a) The volume of an aqueous solution of NaCl at 25 degree C was measured at series of molalities b, and it was found that the volume fitted the expression v = 1003 + 16.62x + 1.77x^3/2 + 0.12x^2 where v = V/cm^3, V is the volume of a solution formed from 1.000 kg water and x = b/b^. Calculate the partial molar volume of the components in a solution of molality 0.100 mol kg^-1. (b) At 18 degree C the total volume V of a solution formed from MgSO_4 and 1.000 kg of water fits the expression v = 1001.21 + 34.69(x - 0.070)^2, where v = V/cm^3 and x = b/bx = b/b^. Calculate the partial molar volumes of the salt and the solvent when in a solution of molality 0.050 mol kg^-1. (a) Suppose that n_A = 0.10n_B and a small change in composition results in mu A changing by delta mu_A = +12 J mol^-1, by how much will mu_B change? (b) Suppose that n_A = 0.22n_B and a small change in composition results in mu_A changing by delta mu_A = 15 J mol^-1, by how much will mu_B change? (a) Consider a container of volume 5.0 dm^3 that is divided into two compartments of equal size. In the left compartment there is nitrogen at 1.0 atm and 25 degree C; in the right compartment there is hydrogen at the same temperature and pressure. Calculate the entropy and Gibbs energy of mixing when the partition is removed. Assume that the gases are perfect. (b) Consider a container of volume 250 cm^3 that is divided into twoExplanation / Answer
Assumption: The system is at constant temperature throughout the changes and only the two components A & B (as specified in the problem) are present in the system.
Approach: To find out the change in µB, we will use Gibbs' Duhem equation for two component systems at constant temperature, which is as follows:
nA µA + nB µB = 0
Rearranging for µB, we get:
µB = - nA µA / nB
Substituting the values specified in the problem, i.e. nA = 0.22*nB and µA = -15 J mol-1, we get:
µB = - 0.22*nB * (-15 J mol-1) / nB
Therefore, µB = - 0.22 * (-15) J mol-1 = 3.30 J mol-1
Hence, µB will change by 3.30 J mol-1. [Final answer]
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