When 1.00g of sodium hydroxide is dissolved in 100.0 g of water in an insulatedcontainer the temperature rises from 20.00°C to 22.66°C. Calculate the enthalpychange for the solution. State any assumptions made.NOTE: Dissolving reactions due not have limiting reagents.
Question
When 1.00g of sodium hydroxide is dissolved in 100.0 g of water in an insulatedcontainer the temperature rises from 20.00°C to 22.66°C. Calculate the enthalpychange for the solution. State any assumptions made.NOTE: Dissolving reactions due not have limiting reagents.
Solution
To calculate the enthalpy change for the solution, we need to use the formula for heat transfer (q) in a chemical reaction:
q = mcΔT
where: m = mass of the substance (in this case, water) c = specific heat capacity of the substance (for water, it's 4.18 J/g°C) ΔT = change in temperature
First, calculate the change in temperature (ΔT):
ΔT = T_final - T_initial = 22.66°C - 20.00°C = 2.66°C
Then, substitute the values into the formula:
q = (100.0 g)(4.18 J/g°C)(2.66°C) = 1113.08 J
The heat absorbed by the water is equal to the heat released by the sodium hydroxide. Therefore, the enthalpy change (ΔH) for the sodium hydroxide is -1113.08 J. However, this is the enthalpy change for the amount of sodium hydroxide that was used (1.00 g). To find the enthalpy change per mole of sodium hydroxide, we need to convert grams to moles and then divide the enthalpy change by the number of moles.
The molar mass of sodium hydroxide (NaOH) is approximately 40.00 g/mol. Therefore, 1.00 g of NaOH is equal to 0.025 mol.
ΔH = -1113.08 J / 0.025 mol = -44,523.2 J/mol
However, enthalpy is usually expressed in kJ/mol, so we need to convert J to kJ:
ΔH = -44.52 kJ/mol
Therefore, the enthalpy change for the solution is -44.52 kJ/mol.
Assumptions made:
- The specific heat capacity of the solution is the same as that of pure water.
- The reaction is carried out under constant pressure.
- All the heat released by the sodium hydroxide is absorbed by the water.
- The dissolving of sodium hydroxide is a completely exothermic process.
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