An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Calculate Δ G for the first reaction using Δ G = Δ H − T Δ S , resulting in Δ G = 3868 J , indicating the reverse reaction is spontaneous.
Calculate Δ S for the second reaction using Δ S = T Δ H − Δ G , resulting in Δ S = 2684 K J .
Determine that the first reaction's reverse is spontaneous because 0"> Δ G > 0 .
Determine that the second reaction is spontaneous because Δ G < 0 . The final answers are 3868 and 2684 .
Explanation
Problem Analysis We are given two chemical reactions and some of their thermodynamic properties at a constant temperature of 51. 0 ∘ C . Our goal is to calculate the missing Gibbs free energy ( Δ G ) for the first reaction and the missing entropy change ( Δ S ) for the second reaction. We will also determine the spontaneity of each reaction based on the sign of Δ G .
Calculating Δ G for Reaction 1 First, let's calculate Δ G for the first reaction. We'll use the formula: Δ G = Δ H − T Δ S where Δ H = − 1648 k J = − 1648000 J , Δ S = − 5096 K J , and T = 51. 0 ∘ C = 51.0 + 273.15 = 324.15 K Substituting these values, we get: Δ G = − 1648000 J − ( 324.15 K ) ( − 5096 K J )
Determining Spontaneity of Reaction 1 Δ G = − 1648000 J + 1651863.4 J = 3863.4 J Rounding to zero decimal places, we have Δ G = 3868 J = 3.868 k J Since 0"> Δ G > 0 , the reverse reaction is spontaneous.
Calculating Δ S for Reaction 2 Next, let's calculate Δ S for the second reaction. We'll use the formula: Δ S = T Δ H − Δ G where Δ H = 852 k J = 852000 J , Δ G = − 18 k J = − 18000 J , and T = 51. 0 ∘ C = 324.15 K .Substituting these values, we get: Δ S = 324.15 K 852000 J − ( − 18000 J ) Δ S = 324.15 K 870000 J = 2683.94 K J Rounding to zero decimal places, we have Δ S = 2684 K J Since Δ G < 0 , the forward reaction is spontaneous.
Final Results In summary, for the first reaction, Δ G = 3868 J , and the reverse reaction is spontaneous. For the second reaction, Δ S = 2684 K J , and the forward reaction is spontaneous.
Examples
Thermodynamics plays a crucial role in chemical engineering, especially in designing and optimizing chemical reactions. For example, consider designing a reactor for producing ammonia ( N H 3 ) from nitrogen and hydrogen. By understanding the enthalpy, entropy, and Gibbs free energy changes, engineers can determine the optimal temperature and pressure conditions for maximizing ammonia production. If the Gibbs free energy change for the reaction is negative, the reaction is spontaneous under those conditions, ensuring a high yield of ammonia. This knowledge helps in creating efficient and cost-effective industrial processes.
