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Question

Consider the equation ∆G = ∆G° + RT ln(Q). What is the value of ∆G for a reaction at equilibrium? What does Q equal at equilibrium? At equilibrium, the previous equation reduces to ∆G° = −RT ln(K). When ∆G° > 0, what does it indicate about K? When ∆G° < 0, what does it indicate about K? When t ∆G° = 0, what does it indicate about K? ∆G predicts spontaneity for a reaction, whereas ∆G° predicts the equilibrium position. Explain what this statement means. Under what conditions can you use ∆G° to determine the spontaneity of a reaction?

Solution Preview

The given equation is http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_604e3260d3ec549f454d6b02cd6b0f43.png.

At equilibrium, http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_ca882b0a73770c50fb3e298efb7d8ee3.png is zero and http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_df7b73e74cd078e1b599e4a29fe09f7c.png becomes http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_4c564fe0304724d3559aaedc95570ad4.png.

Therefore, the value of http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_60581dd77405fc26b0adb279f99d0792.png.

When http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_dd4d8a010037ffce2eaddcf436f66f02.png, http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_4c564fe0304724d3559aaedc95570ad4.png will be less than http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_ed6a7e399a7053bc1d5d1e93a0dedfa2.png.

When http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_dd4d8a010037ffce2eaddcf436f66f02.png, http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_4f3966527cfb2eb94fe3c596c8bc78c8.png which is less than one.

When http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_e2f8cfa803c1f8590505346b4fdd68fe.png, http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_59526f276d107fc80fa0bc49b6516e06.png which is greater than one.

When http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_f2ae3886c35fd0ca20b6ee9f8b1a88eb.png, http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_f3c47517827db1fb16f6f5d5e33942af.png.

The http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_ca882b0a73770c50fb3e298efb7d8ee3.png predicts the spontaneity for a reaction, whereas http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_1efd1fab5ac19b0b5231d7b55426c553.png predicts the equilibrium position. The http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_ca882b0a73770c50fb3e298efb7d8ee3.png predicts the spontaneity for a reaction. When http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_ca882b0a73770c50fb3e298efb7d8ee3.png is less than zero, the reaction is spontaneous, whereas when http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_ca882b0a73770c50fb3e298efb7d8ee3.png is more than zero, the reaction is not spontaneous. The http://seo-question-images.s3-website-us-east-1.amazonaws.com/9781305079243/79243-16-8RQ/img_4bdc0d5f8d00632f05699846e799309c.png predicts the feasibility of a reaction. If it is less than zero then forward reaction is favored and the reaction becomes spontaneous. If it is greater than zero, reaction shifts in backward direction and become non spontaneous.

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