Get comprehensive solutions to your problems with IDNLearn.com. Get prompt and accurate answers to your questions from our community of experts who are always ready to help.
Sagot :
Certainly! Let's approach this problem step by step, utilizing Hess's law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the intermediate steps that lead to the overall reaction.
### Given Reactions and Enthalpy Changes:
1. Intermediate Reaction 1:
[tex]\[ CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g) \quad \Delta H_1 = -802\, \text{kJ} \][/tex]
2. Intermediate Reaction 2:
[tex]\[ 2H_2O(g) \rightarrow 2H_2O(l) \quad \Delta H_2 = -88\, \text{kJ} \][/tex]
3. Overall Reaction:
[tex]\[ CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l) \quad \Delta H_{\text{overall}} = -890\, \text{kJ} \][/tex]
### Using Hess's Law:
To determine the correctness of the enthalpy diagram, we sum the enthalpy changes of the intermediate reactions and ensure they match the overall enthalpy change for the reaction.
[tex]\[ \Delta H_{\text{calculated overall}} = \Delta H_1 + \Delta H_2 = -802\, \text{kJ} + (-88\, \text{kJ}) = -890\, \text{kJ} \][/tex]
### Check for Correctness:
We see that:
[tex]\[ \Delta H_{\text{calculated overall}} = -890\, \text{kJ} = \Delta H_{\text{overall}} \][/tex]
This confirms the enthalpy diagram is correct according to Hess's law.
### Enthalpy Diagram:
The enthalpy diagram represents the changes in enthalpy for the reactions in a visual manner. It can be sketched as follows:
1. Start with [tex]\(CH_4(g) + 2O_2(g)\)[/tex]:
- The initial enthalpy level for [tex]\(CH_4(g) + 2O_2(g)\)[/tex].
2. After the first reaction:
- The system releases [tex]\(-802\, \text{kJ}\)[/tex], dropping to the enthalpy level of [tex]\(CO_2(g) + 2H_2O(g)\)[/tex].
3. After the second reaction:
- The system releases an additional [tex]\(-88\, \text{kJ}\)[/tex], reaching the final enthalpy level of the overall reaction [tex]\(CO_2(g) + 2H_2O(l)\)[/tex].
This can be summarized in the following diagram:
[tex]\[ \begin{array}{rcl} CH_4(g) + 2O_2(g) & & \\ & \downarrow & \text{(-802 kJ)} \\ CO_2(g) + 2H_2O(g) & & \\ & \downarrow & \text{(-88 kJ)} \\ CO_2(g) + 2H_2O(l) & & \\ \end{array} \][/tex]
Hence, the enthalpy diagram is:
[tex]\[ \begin{array}{rcl} CH_4(g) + 2O_2(g) & \quad & \\ & & \\ -802 \text{kJ} & & \\ & & -890\, \text{kJ} \\ CO_2(g) + 2H_2O(g) & & \\ & & -88 \text{kJ} \\ CO_2(g) + 2H_2O(l) & & \\ \end{array} \][/tex]
This diagram correctly represents the enthalpy changes for the intermediate and overall reactions, confirming the validity of the given enthalpy values.
### Given Reactions and Enthalpy Changes:
1. Intermediate Reaction 1:
[tex]\[ CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g) \quad \Delta H_1 = -802\, \text{kJ} \][/tex]
2. Intermediate Reaction 2:
[tex]\[ 2H_2O(g) \rightarrow 2H_2O(l) \quad \Delta H_2 = -88\, \text{kJ} \][/tex]
3. Overall Reaction:
[tex]\[ CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l) \quad \Delta H_{\text{overall}} = -890\, \text{kJ} \][/tex]
### Using Hess's Law:
To determine the correctness of the enthalpy diagram, we sum the enthalpy changes of the intermediate reactions and ensure they match the overall enthalpy change for the reaction.
[tex]\[ \Delta H_{\text{calculated overall}} = \Delta H_1 + \Delta H_2 = -802\, \text{kJ} + (-88\, \text{kJ}) = -890\, \text{kJ} \][/tex]
### Check for Correctness:
We see that:
[tex]\[ \Delta H_{\text{calculated overall}} = -890\, \text{kJ} = \Delta H_{\text{overall}} \][/tex]
This confirms the enthalpy diagram is correct according to Hess's law.
### Enthalpy Diagram:
The enthalpy diagram represents the changes in enthalpy for the reactions in a visual manner. It can be sketched as follows:
1. Start with [tex]\(CH_4(g) + 2O_2(g)\)[/tex]:
- The initial enthalpy level for [tex]\(CH_4(g) + 2O_2(g)\)[/tex].
2. After the first reaction:
- The system releases [tex]\(-802\, \text{kJ}\)[/tex], dropping to the enthalpy level of [tex]\(CO_2(g) + 2H_2O(g)\)[/tex].
3. After the second reaction:
- The system releases an additional [tex]\(-88\, \text{kJ}\)[/tex], reaching the final enthalpy level of the overall reaction [tex]\(CO_2(g) + 2H_2O(l)\)[/tex].
This can be summarized in the following diagram:
[tex]\[ \begin{array}{rcl} CH_4(g) + 2O_2(g) & & \\ & \downarrow & \text{(-802 kJ)} \\ CO_2(g) + 2H_2O(g) & & \\ & \downarrow & \text{(-88 kJ)} \\ CO_2(g) + 2H_2O(l) & & \\ \end{array} \][/tex]
Hence, the enthalpy diagram is:
[tex]\[ \begin{array}{rcl} CH_4(g) + 2O_2(g) & \quad & \\ & & \\ -802 \text{kJ} & & \\ & & -890\, \text{kJ} \\ CO_2(g) + 2H_2O(g) & & \\ & & -88 \text{kJ} \\ CO_2(g) + 2H_2O(l) & & \\ \end{array} \][/tex]
This diagram correctly represents the enthalpy changes for the intermediate and overall reactions, confirming the validity of the given enthalpy values.
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.
