Calculate the internal energy change, Δ_rU, for the combustion of 6.9261 g of diethylene glycol (C₄H₁₀O₃, molar mass = 106.120 g mol^-1) if the combustion inside a bomb calorimeter, C_cal = 13.84 kJ °C^-1, causes a temperature change from 22.8 °C to 34.0 °C.

Question

Quizplus · Accepted Answer

First, we need to calculate the heat transferred in the bomb calorimeter using the formula:
q = CΔT
where q is the heat transferred, C is the calorimeter constant (given as 13.84 kJ/°C), and ΔT is the change in temperature (34.0 °C -22.8 °C = 11.2 °C).

q = (13.84 kJ/°C) * 11.2 °C = 154.88 kJ

Next, we need to convert the mass of diethylene glycol to moles using the molar mass given:
moles = mass/molar mass = 6.9261 g / 106.120 g/mol = 0.06527 mol

Then, we can use the formula for the internal energy change of combustion:
ΔU = -q/n
where n is the number of moles of diethylene glycol combusted.

ΔU = -154.88 kJ / 0.06527 mol = -2371.26 J/mol

Finally, we need to convert the units to kJ/mol:
ΔU = -2.37126 kJ/mol

Rounding to two significant figures, the answer is -2.4 kJ/mol, which corresponds to answer choice C (-2.37 × 10^3 J/mol or -2.37 kJ/mol).

Calculate the Internal Energy Change, ΔrU, for the Combustion of 6.9261

Calculate the Internal Energy Change, Δ_rU, for the Combustion of 6.9261