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A total of 2.00 mol of a compound is allowed to react with water in a foam coffee cup and the reaction produces 126 g of solution. The reaction caused the temperature of the solution to rise from 21.00 to 24.70 ∘C. What is the enthalpy of this reaction? Assume that no heat is lost to the surroundings or to the coffee cup itself and that the specific heat of the solution is the same as that of pure water. Enter your answer in kilojoules per mole of compound to three significant figures.

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Answer:

  • 0.976 kJ/mol

Explanation:

A foam coffe cup is considered a perfectly insulated system: heat energy is not exchanged with the surroundings.

Under that assumption, the heat released by the chemical reaction is equal to the heat absorbed by the system.

1. Heat absorbed by the system:

Use the equation Heat = Q = m × C × ΔT, with:

  • m = 126 g (the amount of solution produced)
  • C = specific heat of pure water = 4.186 J/gºC
  • ΔT = increase of temperature = 24.70 ºC - 21.00ºC = 3.70ºC

Q = 126g × 4.186J/gºC × 3.70ºC = 1,951.5J

2. Enthalpy of the reaction

The enthalpy must be reported in kJ/mol.

Then, convert juoles to kilojoules, dividing by 1,000; and divide by 2.00 moles, which is the amount of compound that reacted:

  • ΔHrxn = 1,951.5J × (1kJ / 1,000J) × (1 / 2mol) ≈ 0.9758 kJ/mol

Round to 3 significant figures: 0.976 kJ/mol

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