A triatomic molecule can have a linear configuration, as does CO 2 (Figure a), o

Question

A triatomic molecule can have a linear configuration, as does CO2 (Figure a), or it can be nonlinear, like H2O (Figure b). Suppose the temperature of a gas of triatomic molecules is sufficiently low that vibrational motion is negligible.

(a) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are linear?
Eint/nT =

(b) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are nonlinear?
Eint/nT =

At high temperatures, a triatomic molecule has two modes of vibration, and each contributes

R

to the molar specific heat for its kinetic energy and another

R

for its potential energy. (c) Identify the high-temperature molar specific heat at constant volume for a triatomic ideal gas of the linear molecules. (Use the following as necessary: R.)
Eint/nT =

(d) Identify the high-temperature molar specific heat at constant volume for a triatomic ideal gas of the nonlinear molecules. (Use the following as necessary: R.)
Eint/nT =

(e) Explain how specific heat data can be used to determine whether a triatomic molecule is linear or nonlinear.

Explanation / Answer

molar specific heat at constant volume = Cv = (f/2)*R

where f = degree of freedoms

(at lower temp)

for H2O

f = 6

Cv = (6/2)*R

for CO2

f = 6

Cv = (6/2)R

at high temp.

for H2O

f = 6 + 3 (due to rotation)

Cv = (9/2)R

for CO2

f = 6 + 4 (due to vibration)

Cv = (10/2)R

(e): if specific heat is high then it is linear molecule and if it is low then it is non linear tri atomic molecule

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