Question

5.000 g of compound x with molecular formula c4h6 are burned in a constant - pressure calorimeter containing 50.00 kg of water at 25°c. the temperature of the water is observed to rise by 1.065°c. (you may assume all the heat released by the reaction is absorbed by the water, and none by the calorimeter itself.) calculate the standard heat of formation of compound x at 25°c. be sure your answer has a unit symbol, if necessary, and round it to 3 significant digits.

Explanation:

Step1: Calculate the heat absorbed by water

The formula for heat absorbed \(q = mc\Delta T\), where \(m = 50.00\space kg=50000\space g\), \(c = 4.18\space J/(g\cdot^{\circ}C)\), \(\Delta T=1.065^{\circ}C\)

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Step2: Calculate the moles of \(C_4H_6\)

The molar mass of \(C_4H_6\): \(M=(4\times12 + 6\times1)\space g/mol=54\space g/mol\)
Moles \(n=\frac{m}{M}=\frac{5.000\space g}{54\space g/mol}\approx0.0926\space mol\)

Step3: Calculate the heat of combustion per mole

\(\Delta H_{comb}=-\frac{q}{n}\) (negative because combustion is exothermic)

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Step4: Use the heat of formation formula

The combustion reaction: \(C_4H_6+\frac{11}{2}O_2 = 4CO_2+3H_2O\)
\(\Delta H_{comb}=\sum n\Delta H_f(products)-\sum n\Delta H_f(reactants)\)
\(\Delta H_f(CO_2)=- 393.5\space kJ/mol\), \(\Delta H_f(H_2O)=- 285.8\space kJ/mol\), \(\Delta H_f(O_2) = 0\space kJ/mol\)

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Answer:

\(23.4\space kJ/mol\)