To find the internal energy of combustion of D-ribose, we'll first determine the calorimeter constant (C) using the data for benzoic acid. We can then use that constant to find the internal energy of combustion for D-ribose. Finally, we'll use this value to calculate the enthalpy of formation.
Step 1: Determine the calorimeter constant (C)
We know the temperature change for benzoic acid (∆T_benzoic) is 1.940K, the mass of benzoic acid (m_benzoic) is 0.825g, and the internal energy of combustion of benzoic acid (ΔU_benzoic) is -3251 kJ/mol. First, we need to convert the mass of benzoic acid to moles. The molar mass of benzoic acid (C7H6O2) is 12*7 + 1*6 + 16*2 = 122g/mol.
Number of moles of benzoic acid (n_benzoic) = m_benzoic / molar mass_benzoic = 0.825g / 122 g/mol = 0.00676 mol
Now we can use the following relation to find the calorimeter constant (C):
C = (n_benzoic * ΔU_benzoic) / ∆T_benzoic = (0.00676 mol * -3251 kJ/mol) / 1.940K ≈ -11.39 kJ/K
Step 2: Calculate the internal energy of combustion for D-ribose
We know the temperature change for D-ribose (∆T_ribose) is 0.910K, and the mass of D-ribose (m_ribose) is 0.727g. First, we need to convert the mass of D-ribose to moles. The molar mass of D-ribose (C5H10O5) is 12*5 + 1*10 + 16*5 = 150g/mol.
Number of moles of D-ribose (n_ribose) = m_ribose / molar mass_ribose = 0.727g / 150 g/mol = 0.00485 mol
Now we can use the following relation to find the internal energy of combustion for D-ribose (ΔU_ribose):
ΔU_ribose = (C * ∆T_ribose) / n_ribose = (-11.39 kJ/K * 0.910K) / 0.00485 mol ≈ -2150 kJ/mol
Step 3: Calculate the enthalpy of formation for D-ribose
Finally, we can determine the enthalpy of formation (ΔH_f) for D-ribose using the internal energy of combustion (ΔU_ribose) and the following relation:
ΔH_f = ΔU_ribose + Δ(ngas) * R * T
D-ribose combusts according to the equation:
C5H10O5 (s) + 5O2 (g) → 5CO2 (g) + 5H2O (l)
The change in moles of gas (Δngas) = 5 (from CO2) - 5 (from O2) = 0. Since Δngas is 0, the enthalpy of formation (ΔH_f) for D-ribose is:
ΔH_f ≈ ΔU_ribose ≈ -2150 kJ/mol
Therefore, the internal energy of combustion of D-ribose is approximately -2150 kJ/mol and its enthalpy of formation is approximately -2150 kJ/mol.
A sample of the sugar D-ribose (C5H10O5) of mass 0.727g was placed in a constant volume calorimeter and then ignited in the prescence of excess oxygen. The temperature rose by 0.910K In a separate experiment in the same calorimeter, the combustion of 0.825g of benzoic acid for which the internal energy of combustion is -3251 KJmol-1 gave a temperature rise of 1.940K. Calculate the internal energy of combustion of D-ribose and its enthalpy of formation.
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