Consider a chemical reaction that has a AH°f = 30.0 kJ/mol and a AS° = 100.0 J//mol•K). At what temperature does this reaction become spontaneous? 2.00 x 102 K 3.00 х 103 к 1.30 х 10? к 7.00 x 101 K 3.00 x 102 K

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**Problem Statement:**

Consider a chemical reaction that has a ΔH° = 30.0 kJ/mol and a ΔS° = 100.0 J/(mol•K). At what temperature does this reaction become spontaneous?

**Options:**

- ○ 2.00 x 10² K
- ○ 3.00 x 10³ K
- ○ 1.30 x 10² K
- ○ 7.00 x 10¹ K
- ○ 3.00 x 10² K

**Explanation:**

To determine the temperature at which the reaction becomes spontaneous, you will use the Gibbs free energy equation:

\[ \Delta G = \Delta H - T \Delta S \]

A reaction is spontaneous when \(\Delta G < 0\).

Given:
- \(\Delta H° = 30.0 \text{ kJ/mol} = 30000 \text{ J/mol}\)
- \(\Delta S° = 100.0 \text{ J/(mol•K)}\)

Set the equation to zero and solve for \(T\):

\[ 0 = 30000 - T \times 100 \]
\[ T = \frac{30000}{100} = 300 \text{ K} \]

Thus, the temperature at which the reaction becomes spontaneous is 300 K.
Transcribed Image Text:**Problem Statement:** Consider a chemical reaction that has a ΔH° = 30.0 kJ/mol and a ΔS° = 100.0 J/(mol•K). At what temperature does this reaction become spontaneous? **Options:** - ○ 2.00 x 10² K - ○ 3.00 x 10³ K - ○ 1.30 x 10² K - ○ 7.00 x 10¹ K - ○ 3.00 x 10² K **Explanation:** To determine the temperature at which the reaction becomes spontaneous, you will use the Gibbs free energy equation: \[ \Delta G = \Delta H - T \Delta S \] A reaction is spontaneous when \(\Delta G < 0\). Given: - \(\Delta H° = 30.0 \text{ kJ/mol} = 30000 \text{ J/mol}\) - \(\Delta S° = 100.0 \text{ J/(mol•K)}\) Set the equation to zero and solve for \(T\): \[ 0 = 30000 - T \times 100 \] \[ T = \frac{30000}{100} = 300 \text{ K} \] Thus, the temperature at which the reaction becomes spontaneous is 300 K.
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