From the data in the table below, calculate A,H and A,U (in kJ•mol ) for the reaction C(s,graphite) + H,0(g) → CO(g) H2(g) at the following conditions. Assume all heat capacities to be constant over the temperature range of interest Standard enthalpies of formation of inorganic and organic compounds at 298 K AH°(kJ-mol¯1) c°m(J•K¯1•mol¯1) pim H20() -285.83 75.291 H20(g) -241.82 33.58 CO(g) -110.53 29.14 H2(g) 28.824 H(g) 217.97 20.784 C(s,graphite) 8.527 C(g) 716.68 20.838 C2(9) 831.90 43.21 (a) 298 K 131.29 kJ•mol¬1 0.0158 X kJ•mol-1 (b) 439 K 133 kJ•mol-1 133 X kJ-mol-1

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I need help with my hw problem. I figured out the delta H for the both temperature, but I cant not figure out how to solve for delta U. 

 

# Calculation of ΔᵣH and ΔᵣU for a Chemical Reaction

## Introduction

This exercise involves calculating the change in enthalpy (ΔᵣH) and the change in internal energy (ΔᵣU) for the reaction:

\[ C_{(s,\text{graphite})} + H_2O_{(g)} \rightarrow CO_{(g)} + H_2_{(g)} \]

The calculations are performed at two different temperatures: 298 K and 439 K. The data provided assumes that all heat capacities remain constant over the temperature range of interest.

## Table of Standard Enthalpies and Heat Capacities

The table below lists the standard enthalpies of formation (\(Δ_fH^\circ\)) and molar heat capacities (\(C^\circ_{p,m}\)) of various substances at 298 K:

| Compound           | \(Δ_fH^\circ\) (kJ·mol⁻¹) | \(C^\circ_{p,m}\) (J·K⁻¹·mol⁻¹) |
|--------------------|----------------------------|----------------------------------|
| \(H_2O (l)\)       | -285.83                    | 75.291                           |
| \(H_2O (g)\)       | -241.82                    | 33.58                            |
| \(CO (g)\)         | -110.53                    | 29.14                            |
| \(H_2 (g)\)        | 0                          | 28.824                           |
| \(H (g)\)          | 217.97                     | 20.784                           |
| \(C_{(s, \text{graphite})}\) | 0                          | 8.527                            |
| \(C (g)\)          | 716.68                     | 20.838                           |
| \(C_2 (g)\)        | 831.90                     | 43.21                            |

## Calculations

### For 298 K

- \(Δ_rH^\circ\) = 131.29 kJ·mol⁻¹ (correct)
- \(Δ_rU^\circ\) = 0.0158 kJ·mol⁻¹ (incorrect)

### For 439 K

- \(Δ_rH^\circ\) = 133 kJ·mol
Transcribed Image Text:# Calculation of ΔᵣH and ΔᵣU for a Chemical Reaction ## Introduction This exercise involves calculating the change in enthalpy (ΔᵣH) and the change in internal energy (ΔᵣU) for the reaction: \[ C_{(s,\text{graphite})} + H_2O_{(g)} \rightarrow CO_{(g)} + H_2_{(g)} \] The calculations are performed at two different temperatures: 298 K and 439 K. The data provided assumes that all heat capacities remain constant over the temperature range of interest. ## Table of Standard Enthalpies and Heat Capacities The table below lists the standard enthalpies of formation (\(Δ_fH^\circ\)) and molar heat capacities (\(C^\circ_{p,m}\)) of various substances at 298 K: | Compound | \(Δ_fH^\circ\) (kJ·mol⁻¹) | \(C^\circ_{p,m}\) (J·K⁻¹·mol⁻¹) | |--------------------|----------------------------|----------------------------------| | \(H_2O (l)\) | -285.83 | 75.291 | | \(H_2O (g)\) | -241.82 | 33.58 | | \(CO (g)\) | -110.53 | 29.14 | | \(H_2 (g)\) | 0 | 28.824 | | \(H (g)\) | 217.97 | 20.784 | | \(C_{(s, \text{graphite})}\) | 0 | 8.527 | | \(C (g)\) | 716.68 | 20.838 | | \(C_2 (g)\) | 831.90 | 43.21 | ## Calculations ### For 298 K - \(Δ_rH^\circ\) = 131.29 kJ·mol⁻¹ (correct) - \(Δ_rU^\circ\) = 0.0158 kJ·mol⁻¹ (incorrect) ### For 439 K - \(Δ_rH^\circ\) = 133 kJ·mol
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