Question

The heat required to raise the temperature of m (kg) of a liquid from T1 to T2 at constant pressure is Z T2CpT dT (1) In high school and in first-year college physics courses, the formula is usually given asQ ΔH m Q mCp ΔT mCpT2 ␣T1 (2)T1(a) What assumption about Cp is required to go from Equation 1 to Equation 2? (b) The heat capacity (Cp) of liquid n-hexane is measured in a bomb calorimeter. A small reaction flask (the bomb) is placed in a well-insulated vessel containing 2.00L of liquid n–C6H14 at T 300 K. A combustion reaction known to release 16.73 kJ of heat takes place in the bomb, and the subsequent temperature rise of the system contents is measured and found to be 3.10 K. In a separate experiment, it is found that 6.14kJ of heat is required to raise the temperature of everything in the system except the hexane by 3.10 K. Use these data to estimate Cp[kJ/(mol K)] for liquid n-hexane at T 300 K, assuming that the condition required for the validity ofEquation 2 is satisfied. Compare your result with a tabulated value.

Answer 1

(a)

dQ = mdq

dq =
`C_p`dT

`q = \int\limits^(T_2)_(T_1) {C_p} \, dT` =
`C_p` (T₂ - T₁)

From the above equations, the underlying assumption is that
`C_p` remains constant with change in temperature.

(b)

Given;

V = 2L

T₁ = 300 K

Q₁ = 16.73 KJ , Q₂ = 6.14 KJ

ΔT = 3.10 K , ΔT₂ = 3.10 K for calorimeter

Let
`C_(cal)` be heat constant of calorimeter

Q₂ =
`C_(cal)` ΔT

Heat absorbed by n-C₆H₁₄ = Q₁ - Q₂

Q₁ - Q₂ = m
`C_p` ΔT

number of moles of n-C₆H₁₄, n = m/M

ρ = 650 kg/m³ at 300 K

M = 86.178 g/mol

m = ρv = 650 (2x10⁻³) = 1.3 kg

n = m/M => 1.3 / 0.086178 = 15.085 moles

Q₁ - Q₂ = m
`C_p`' ΔT

`C_p` = (16.73 - 6.14) / (15.085 x 3.10)

`C_p` = 0.22646 KJ mol⁻¹ k⁻¹