The effect of volatiles on the measurement of the reaction heat by differential scanning calorimetry

Abstract

When gases evolve during a chemical reaction, a fraction of the reaction heat is lost with them. We have analyzed, both theoretically and experimentally, the deviations that this effect can produce on the determination of the reaction heat by differential scanning calorimetry (DSC). It is shown that, even in the absence of gas overheating, deviations related to variations in the sample heat capacity can be substantial in experiments involving very intense DSC peaks. However, experiments performed on thermal decomposition of metal organic salts and on evaporation of liquids have shown that deviations usually arise from gas overheating.

Appendix

Calculation of ΔQ _P and ΔQ _C

We need to calculate the third term on the right-hand side of Eq. 10:

$$ \Delta Q_{\text{C}} +\Delta Q_{\text{P}} = R\mathop \int \nolimits \left( {C_{\text{REF}} - C} \right){\text{dDSC}}. $$

(18)

Integration by parts and substitution of C by its value of Eq. 5 leads to:

$$ \Delta Q_{\text{C}} +\Delta Q_{\text{P}} = R\left( {C_{\text{REF}} + C_{\text{B}} } \right){\text{DSC}}_{\text{f}} - R\left( {C_{\text{REF}} + C_{\text{A}} } \right){\text{DSC}}_{\text{i}} + R(C_{\text{A}} - C_{\text{B}} )\int {{\text{DSC}}\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} {\text{d}}t} , $$

(19)

where “i” and “f” refer to the value before and after the DSC peak. ΔQ _C is the addition of the first two terms. If we take into account that

$$ {\text{DSC}}_{{{\text{f,}}\,{\text{i}}}} = - (C_{\text{REF}} + C_{{{\text{B}},{\text{A}}}} )\beta , $$

(20)

and consider that, usually,

$$ C_{\text{REF}} + C_{\text{B}} \cong C_{\text{REF}} + C_{\text{A}} , $$

(21)

we arrive to the desired result:

$$ \Delta Q_{\text{C}} \cong R(C_{\text{REF}} + C_{\text{A}} )( C_{\text{A}} - C_{\text{B}} )\beta , $$

(22)

where R(C _REF + C _A) is the DSC time constant τ _SIGNAL [3] at the beginning of the reaction. For reactions involving gas evolution, R (C _REF + C _A) > τ _SIGNAL.

The last term in Eq. 19 is ΔQ _P. In general, α can be obtained from a TG curve (Eq. 6). In those cases where the time response of the DSC signal is short enough, use of Eq. 7 leads to the desired result:

$$ \Delta Q_{\text{P}} = \frac{{R(C_{\text{A}} - C_{\text{B}} )}}{Q}\int {{\text{DSC}} \cdot {\text{DSC}}_{\text{P}} {\text{d}}t} . $$

(23)