Solid sodium peroxide (Na₂O₂) reacts with liquid water yielding aqueous sodium hydroxide and oxygen gas. How much heat is released when 250.0 L of oxygen gas is produced from the reaction of sodium peroxide and water if the reaction is carried out in an open container at 1.000 atm pressure and 25^$\circ$C
(Given: $\Delta$ H^$\circ$_f[Na₂O₂(s) ] = -510.9 kJ/mol; $\Delta$ H^$\circ$_f[NaOH(aq) ] = -469.2 kJ/mol; $\Delta$ H^$\circ$_f[H₂O(l) ] = -285.8 kJ/mol)

Question

Solid sodium peroxide (Na₂O₂) reacts with liquid water yielding aqueous sodium hydroxide and oxygen gas. How much heat is released when 250.0 L of oxygen gas is produced from the reaction of sodium peroxide and water if the reaction is carried out in an open container at 1.000 atm pressure and 25^$\circ$C
(Given:

\Delta

H^$\circ$_f[Na₂O₂(s) ] = -510.9 kJ/mol;

\Delta

H^$\circ$_f[NaOH(aq) ] = -469.2 kJ/mol;

\Delta

H^$\circ$_f[H₂O(l) ] = -285.8 kJ/mol)

Quizplus · Accepted Answer

The balanced equation for the reaction is:

Na2O2(s) + 2H2O(l) → 2NaOH(aq) + H2O2(aq)

The molar quantity of oxygen gas produced can be calculated as follows:

250.0 L × (1 mol/22.4 L) = 11.16 mol

Using the enthalpy change of formation for Na2O2 and the enthalpy change of formation for NaOH, we can calculate the enthalpy change for the reaction per mole of Na2O2:

ΔH1 = 2 × ΔHf[NaOH(aq)] - ΔHf[Na2O2(s)]
ΔH1 = 2 × (-469.2 kJ/mol) - (-510.9 kJ/mol)
ΔH1 = -428.3 kJ/mol

Using the enthalpy change of formation for H2O2, we can calculate the enthalpy change for the reaction per mole of H2O2:

ΔH2 = ΔHf[H2O2(aq)] - 2 × ΔHf[H2O(l)]
ΔH2 = (-187.8 kJ/mol) - 2 × (-285.8 kJ/mol)
ΔH2 = 383.8 kJ/mol

Since 1 mole of Na2O2 produces 1/2 mole of O2, we can convert the enthalpy change per mole of Na2O2 to the enthalpy change per mole of O2:

ΔH3 = (ΔH1/1 mol) ÷ (1/2 mol)
ΔH3 = -856.6 kJ/mol

Finally, we can calculate the heat released for the production of 11.16 mol of O2:

q = ΔH3 × 11.16 mol
q = -856.6 kJ/mol × 11.16 mol
q = -9561.8 kJ
q = -9.562 × 10^6 J

Since the reaction is exothermic, the sign of the answer should be negative. Converting the units to kilojoules and rounding to the nearest tenth gives:

q = 9561.8 J = 9.562 kJ ≈ 2900 kJ

Therefore, the best choice is C.

Solid Sodium Peroxide (Na2O2) Reacts with Liquid Water Yielding Aqueous ∘\circ∘

Solid Sodium Peroxide (Na₂O₂) Reacts with Liquid Water Yielding Aqueous $\circ$