Calculate the enthalpy change (kJ) when 40.0 g of [tex]$Na_2 O_2$[/tex] reacts with excess water?
Report your answer with the correct number of significant figures. Do not include units in your answer.
Answer (2)
The enthalpy change when 40.0 g of sodium peroxide (Na2O2) reacts with excess water is -32.3 kJ. This value is calculated using the molar mass of Na2O2 and stoichiometry from the balanced chemical reaction. Therefore, the reaction is exothermic, releasing energy.
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Calculate the molar mass of N a 2 O 2 : 2 ( 22.99 ) + 2 ( 16.00 ) = 77.98 g/mol.
Calculate the moles of N a 2 O 2 : 77.98 40.0 = 0.513 mol.
Use the stoichiometry to find the enthalpy change: $\frac{0.513}{2}
imes -126 = -32.3$ kJ.
The enthalpy change when 40.0 g of N a 2 O 2 reacts with excess water is − 32.3 .
Explanation
Problem Setup and Given Information We are given the balanced chemical equation: 2 N a 2 O 2 ( s ) + 2 H 2 O ( l ) → 4 N a O H ( s ) + O 2 ( g ) and the enthalpy change for the reaction, Δ H ∘ = − 126 k J for 2 moles of N a 2 O 2 reacting. We need to calculate the enthalpy change when 40.0 g of N a 2 O 2 reacts with excess water.
Calculating Molar Mass of Sodium Peroxide First, we need to calculate the molar mass of N a 2 O 2 . The molar mass of sodium (Na) is 22.99 g/mol, and the molar mass of oxygen (O) is 16.00 g/mol. Therefore, the molar mass of N a 2 O 2 is: M o l a r ma ss ( N a 2 O 2 ) = 2 × 22.99 + 2 × 16.00 = 45.98 + 32.00 = 77.98 g / m o l
Calculating Moles of Sodium Peroxide Next, we calculate the number of moles of N a 2 O 2 in 40.0 g using the formula: m o l es = m o l a r ma ss ma ss m o l es ( N a 2 O 2 ) = 77.98 g / m o l 40.0 g = 0.51295 m o l Rounding to three significant figures, we have 0.513 mol.
Calculating Enthalpy Change Now, we use the stoichiometry of the reaction to determine the enthalpy change for the calculated moles of N a 2 O 2 . The given enthalpy change is for 2 moles of N a 2 O 2 . We set up a proportion: m o l e s N a 2 O 2 Δ H = 2 m o l es − 126 k J Δ H = 2 m o l es − 126 k J × 0.513 m o l es = − 32.319 k J Rounding to three significant figures, the enthalpy change is -32.3 kJ.
Final Answer Therefore, the enthalpy change when 40.0 g of N a 2 O 2 reacts with excess water is -32.3 kJ.
Examples
This calculation is crucial in designing chemical processes involving sodium peroxide, such as in emergency oxygen generators or bleaching processes. Knowing the enthalpy change helps engineers manage heat release or absorption, ensuring safety and efficiency. For instance, if a process releases too much heat (exothermic), it might require cooling systems to prevent overheating or explosions. Similarly, if a process absorbs too much heat (endothermic), it might need a heating system to maintain the reaction rate. Therefore, understanding enthalpy changes is vital for the safe and effective application of chemical reactions in various industrial and scientific contexts.
