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.
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.
To calculate the internal energy of combustion of D-ribose and its enthalpy of formation, we need to use the concept of Hess's Law, which states that the enthalpy change of a reaction is independent of the pathway taken.
First, let's calculate the heat absorbed by the calorimeter for the combustion of benzoic acid:
q1 = (mass of benzoic acid) * (change in temperature)
= 0.825g * 1.940K
Next, let's calculate the heat absorbed by the calorimeter for the combustion of D-ribose:
q2 = (mass of D-ribose) * (change in temperature)
= 0.727g * 0.910K
Since the calorimeter is a closed system and no heat is exchanged with the surroundings (constant volume calorimeter), the heat absorbed by the calorimeter during the combustion reactions is equal to the heat released by the combustion reactions themselves.
Therefore, the heat of combustion of benzoic acid (ΔH1) is equal to the heat absorbed by the calorimeter during the combustion of benzoic acid:
ΔH1 = -q1
Similarly, the heat of combustion of D-ribose (ΔH2) is equal to the heat absorbed by the calorimeter during the combustion of D-ribose:
ΔH2 = -q2
The enthalpy change of formation of D-ribose (ΔHf) can be calculated using the equation:
ΔHf = ΔH1 - ΔH2
Now, let's calculate the values:
q1 = 0.825g * 1.940K = 1.5975 KJ
q2 = 0.727g * 0.910K = 0.66217 KJ
ΔH1 = -q1 = -1.5975 KJ
ΔH2 = -q2 = -0.66217 KJ
ΔHf = ΔH1 - ΔH2
= -1.5975 KJ - (-0.66217 KJ)
= -0.93533 KJ
Therefore, the internal energy of combustion of D-ribose is approximately -0.93533 KJ, and its enthalpy of formation is also approximately -0.93533 KJ.
To calculate the internal energy of combustion (ΔU) of D-ribose and its enthalpy of formation (ΔHf), we need to use the information provided about the mass, temperature rise, and the internal energy of combustion of benzoic acid.
Let's start by calculating the moles of benzoic acid combusted:
Molar mass of benzoic acid (C6H5COOH) = 122.12 g/mol
Mass of benzoic acid used = 0.825 g
Moles of benzoic acid used = mass / molar mass
= 0.825 g / 122.12 g/mol
Now we can calculate the internal energy change (ΔU) for the combustion of benzoic acid:
ΔU (benzoic acid) = ΔU/mol * moles of benzoic acid combusted
Given:
ΔU (benzoic acid) = -3251 kJ/mol
moles of benzoic acid combusted = 0.825 g / 122.12 g/mol
ΔU (benzoic acid) = -3251 kJ/mol * (0.825 g / 122.12 g/mol)
Next, we can calculate the moles of D-ribose used. Since the molar ratio between benzoic acid and D-ribose can be inferred from the chemical equation of combustion, we can use the moles of benzoic acid combusted to calculate the moles of D-ribose combusted.
Now, let's calculate the moles of D-ribose combusted:
Given:
Molar ratio of benzoic acid to D-ribose = 1:1
moles of benzoic acid combusted = 0.825 g / 122.12 g/mol
moles of D-ribose combusted = moles of benzoic acid combusted
Now, we can calculate the internal energy change (ΔU) for the combustion of D-ribose:
Given:
Mass of D-ribose used = 0.727 g
Temperature rise = 0.910 K
ΔU (D-ribose) = ΔU/mol * moles of D-ribose combusted
ΔU (D-ribose) = ΔU (benzoic acid)
Now that we have ΔU (D-ribose), we can calculate the enthalpy of formation (ΔHf) of D-ribose using the equation:
ΔU (D-ribose) = ΔHf + Δn * RT
Where:
Δn = change in moles of gas (assuming Δn = 0 for this case)
R = ideal gas constant
Now, rearranging the equation, we can solve for ΔHf:
ΔHf = ΔU (D-ribose) - Δn * RT
Since Δn is assumed to be zero and R is a constant, we can simplify the equation to:
ΔHf = ΔU (D-ribose)
Substituting the value of ΔU (D-ribose) calculated earlier will give us the enthalpy of formation of D-ribose.