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Chapter 5: Q. 5.78 (page 206)

Because osmotic pressures can be quite large, you may wonder whether the approximation made in equation5.74is valid in practice: Is 渭0really a linear function of Pto the required accuracy? Answer this question by discussing whether the derivative of this function changes significantly, over the relevant pressure range, in realistic examples.

渭0T,P2鈮�渭0T,P1+P2-P1鈭�渭0鈭�P......equation(5.74)

Short Answer

Expert verified

If a solution has high density then it will produces more pressure than the solution of low density.

Step by step solution

01

Given information

We have been given the difference between pressures

02

Explanation

It does not matter how large the osmotic pressure is 渭0T,P2鈮�渭0T,P1+P2-P1鈭�渭0鈭�P鈥�鈥�equation(5.74),

If the pressure in two parts of the system does not change significantly,

So we can say that the derivative of the function does not change significantly.

Therefore, we can say that an approximation is good enough.

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Most popular questions from this chapter

Functions encountered in physics are generally well enough behaved that their mixed partial derivatives do not depend on which derivative is taken first. Therefore, for instance,

鈭�鈭�V鈭�U鈭�S=鈭�鈭�S鈭�U鈭�V

where each 鈭�/鈭�Vis taken with Sfixed, each 鈭�/鈭�Sis taken with Vfixed, and Nis always held fixed. From the thermodynamic identity (forU) you can evaluate the partial derivatives in parentheses to obtain

鈭�T鈭�VS=-鈭�P鈭�SV

a nontrivial identity called a Maxwell relation. Go through the derivation of this relation step by step. Then derive an analogous Maxwell relation from each of the other three thermodynamic identities discussed in the text (for H,F,andG ). Hold N fixed in all the partial derivatives; other Maxwell relations can be derived by considering partial derivatives with respect to N, but after you've done four of them the novelty begins to wear off. For applications of these Maxwell relations, see the next four problems.

Suppose that a hydrogen fuel cell, as described in the text, is to be operated at 75掳Cand atmospheric pressure. We wish to estimate the maximum electrical work done by the cell, using only the room temperature data at the back of this book. It is convenient to first establish a zero-point for each of the three substances, H2,O2,andH2O. Let us take Gfor both H2andO2to be zero at 25掳C, so that G for a mole of H2Ois -237KJat 25掳C.

(a) Using these conventions, estimate the Gibbs free energy of a mole of H2at 75掳C. Repeat for O2andH2O.

(b) Using the results of part (a), calculate the maximum electrical work done by the cell at 75掳C, for one mole of hydrogen fuel. Compare to the ideal performance of the cell at25掳C.

Use the Clausius-Clapeyron relation to derive equation 5.90 directly from Raoult's law. Be sure to explain the logic carefully.

The standard enthalpy change upon dissolving one mole of oxygen at 25掳C is -11.7 kJ. Use this number and the van't Hoff equation (Problem 5.85) to calculate the equilibrium (Henry's law) constant for oxygen in water at 0掳C and at 100掳 C. Discuss the results briefly.

Plumber's solder is composed of 67% lead and 33% tin by weight. Describe what happens to this mixture as it cools, and explain why this composition might be more suitable than the eutectic composition for joining pipes.
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