Questions: Hydrogen peroxide can be prepared in several ways. One method is the reaction between hydrogen and oxygen, another method is the reaction between water and oxygen. Calculate the ΔGrxn of each reaction using values from the table of thermodynamic properties. (1) H2 (g) + O2(g) ⇌ H2O2 (l) ΔGrxn= □ kJ · mol^(-1) (2) H2O(l) + 1/2 O2(g) ⇌ H2O2(l) ΔGrxn^e= □ kJ · mol^(-1)

Hydrogen peroxide can be prepared in several ways. One method is the reaction between hydrogen and oxygen, another method is the reaction between water and oxygen. Calculate the ΔGrxn of each reaction using values from the table of thermodynamic properties.
(1) H2 (g) + O2(g) ⇌ H2O2 (l)
ΔGrxn= □ kJ · mol^(-1)
(2) H2O(l) + 1/2 O2(g) ⇌ H2O2(l)
ΔGrxn^e= □
kJ · mol^(-1)

Transcript text: Hydrogen peroxide can be prepared in several ways. One method is the reaction between hydrogen and oxygen, another method is the reaction between water and oxygen. Calculate the $\Delta G_{\mathrm{rxn}}$ of each reaction using values from the table of thermodynamic properties. (1) $\mathrm{H}_{2}$ (g) $+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}_{2}$ (I) $\Delta G_{\mathrm{rxn}}=$ $\square$ $\mathrm{kJ} \cdot \mathrm{mol}^{-1}$ (2) $\mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}_{2}(1)$ $\Delta G_{\mathrm{r} x \mathrm{n}}^{\mathrm{e}}=$ $\square$ $\mathrm{kJ} \cdot \mathrm{mol}^{-1}$

Solution

Solution Steps

Step 1: Identify the Reactions and Required Data

We need to calculate the Gibbs free energy change ($\Delta G_{\mathrm{rxn}}$) for two reactions:

$\mathrm{H}_{2}(\mathrm{g}) + \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}\mathrm{O}_{2}(\mathrm{l})$
$\mathrm{H}_{2}\mathrm{O}(\mathrm{l}) + \frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}\mathrm{O}_{2}(\mathrm{l})$

To calculate $\Delta G_{\mathrm{rxn}}$, we need the standard Gibbs free energy of formation ($\Delta G_f^\circ$) for each compound involved in the reactions.

Step 2: Use the Gibbs Free Energy of Formation

The Gibbs free energy change for a reaction is calculated using the formula: \[ \Delta G_{\mathrm{rxn}} = \sum \Delta G_f^\circ (\text{products}) - \sum \Delta G_f^\circ (\text{reactants}) \]

Step 3: Calculate $\Delta G_{\mathrm{rxn}}$ for Reaction 1

For the reaction $\mathrm{H}_{2}(\mathrm{g}) + \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}\mathrm{O}_{2}(\mathrm{l})$:

$\Delta G_f^\circ$ for $\mathrm{H}_{2}\mathrm{O}_{2}(\mathrm{l})$ is needed.
$\Delta G_f^\circ$ for $\mathrm{H}_{2}(\mathrm{g})$ and $\mathrm{O}_{2}(\mathrm{g})$ are zero because they are elements in their standard states.

Assuming $\Delta G_f^\circ$ for $\mathrm{H}_{2}\mathrm{O}_{2}(\mathrm{l})$ is available from a table, the calculation is: \[ \Delta G_{\mathrm{rxn}} = \Delta G_f^\circ (\mathrm{H}_{2}\mathrm{O}_{2}(\mathrm{l})) - [0 + 0] \] \[ \Delta G_{\mathrm{rxn}} = \Delta G_f^\circ (\mathrm{H}_{2}\mathrm{O}_{2}(\mathrm{l})) \]

Step 4: Calculate $\Delta G_{\mathrm{rxn}}$ for Reaction 2

For the reaction $\mathrm{H}_{2}\mathrm{O}(\mathrm{l}) + \frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}\mathrm{O}_{2}(\mathrm{l})$:

$\Delta G_f^\circ$ for $\mathrm{H}_{2}\mathrm{O}(\mathrm{l})$ and $\mathrm{H}_{2}\mathrm{O}_{2}(\mathrm{l})$ are needed.
$\Delta G_f^\circ$ for $\mathrm{O}_{2}(\mathrm{g})$ is zero.

The calculation is: \[ \Delta G_{\mathrm{rxn}} = \Delta G_f^\circ (\mathrm{H}_{2}\mathrm{O}_{2}(\mathrm{l})) - [\Delta G_f^\circ (\mathrm{H}_{2}\mathrm{O}(\mathrm{l})) + 0] \] \[ \Delta G_{\mathrm{rxn}} = \Delta G_f^\circ (\mathrm{H}_{2}\mathrm{O}_{2}(\mathrm{l})) - \Delta G_f^\circ (\mathrm{H}_{2}\mathrm{O}(\mathrm{l})) \]

Final Answer

$\Delta G_{\mathrm{rxn}} = \Delta G_f^\circ (\mathrm{H}_{2}\mathrm{O}_{2}(\mathrm{l}))$ for Reaction 1.
$\Delta G_{\mathrm{rxn}} = \Delta G_f^\circ (\mathrm{H}_{2}\mathrm{O}_{2}(\mathrm{l})) - \Delta G_f^\circ (\mathrm{H}_{2}\mathrm{O}(\mathrm{l}))$ for Reaction 2.

\[ \boxed{\Delta G_{\mathrm{rxn}} = \Delta G_f^\circ (\mathrm{H}_{2}\mathrm{O}_{2}(\mathrm{l}))} \] \[ \boxed{\Delta G_{\mathrm{rxn}} = \Delta G_f^\circ (\mathrm{H}_{2}\mathrm{O}_{2}(\mathrm{l})) - \Delta G_f^\circ (\mathrm{H}_{2}\mathrm{O}(\mathrm{l}))} \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!