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CHM-13

Heat capacity q = n Cp ΔT

q = n Cp ΔT at constant pressure.

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ThermochemistryCalorimetry

Governing equation

q=nCpΔTq=n C_p\Delta T

ΔT∈[−80,200]\Delta T \in \left[-80, 200\right]

where

n
Amount (mol)
C_p
Molar heat capacity (J/(mol·K))
\Delta T
Temperature rise (K)
q
Heat (kJ)

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CHM-13 · phase
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①

Governing law — red

q=nCpΔTq=n C_p\Delta T

ΔT∈[−80,200]\Delta T \in \left[-80, 200\right]

ΔT=−80\Delta T = -80q=−12q = -12

②

Domain of the variable — blue

ΔTmin⁡=−80,ΔTmax⁡=200\Delta T_{\min} = -80,\quad \Delta T_{\max} = 200

ΔT∈[−80,200]\Delta T \in \left[-80, 200\right]

ΔT=−80\Delta T = -80ΔT=−80\Delta T = -80

③

Response curve — green

q=nCpΔTq=n C_p\Delta T

ΔT∈[−80,200]\Delta T \in \left[-80, 200\right]

ΔT=−80\Delta T = -80q=−12q = -12

④

Rate of change — amber

dqdΔT\frac{\mathrm{d}q}{\mathrm{d}\Delta T}

ΔT∈[−80,200]\Delta T \in \left[-80, 200\right]

ΔT=−78.24\Delta T = -78.24q′=0.15q^{\prime} = 0.15

Lecture brief

Historical brief

Ideal-gas law, van ’t Hoff, Nernst, Michaelis–Menten and Clausius–Clapeyron are physical chemistry’s working equations of equilibrium and rate. The lab is pressure, potential and kinetics. This sheet (CHM-13 — Heat capacity q = n Cp ΔT) is the form associated with Calorimetry. Working symbols: nn, CpC_p, ΔT\Delta T →\rightarrow qq. Cp = (∂H/∂T)_p. For an ideal gas Cp − Cv = R.

Purpose

Purpose: compute qq from nn, CpC_p, ΔT\Delta T in Physical chemistry via q=nCpΔTq=n C_p\Delta T q = n Cp ΔT at constant pressure. Use it when a real physical chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given n=2.000 moln = 2.000\,\mathrm{mol}, Cp=75.000 J/(mol⋅K)C_p = 75.000\,\mathrm{J/(mol·K)}, ΔT=10.000 K\Delta T = 10.000\,\mathrm{K}, the governing relation q=nCpΔTq=n C_p\Delta T yields q=1.500 kJq = 1.500\,\mathrm{kJ}. Constant Cp, no phase change in the interval. Move a slider: the numbers are this situation, not a canned story.

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Outputs

  • Heat q1.500 kJ
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CHM-13 · phase
00:0 / 00:08

Narration of this film

Constant Cp, no phase change in the interval.

Cp = (∂H/∂T)_p. For an ideal gas Cp − Cv = R.

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