The difference lies in what the question is asking.

For 9.7 part a, the question asks for the entropy change at a constant pressure with a change in temperature. For this we use the known equation

where C

_{p} is the specific heat of a gas at constant pressure.

For 9.11, the question asks for the entropy change at a constant temperature with a change in pressure. For this, we can use

where R is the gas constant. As the solution manual states, we can rewrite that equation

since P is the inverse of V for ideal gases.

To summarize, it all really depends on what the question asks. Hope I helped!