question_answer 15)

Given below are observations on molar specific heats at room temperature of some common gases. Gas Molar specific heat \[m'=\frac{mc\vartriangle T}{L}=\frac{2500\times 0\cdot 39\times 500}{335}=1500g=1\cdot 5kg\]\[0\cdot 20\] Hydrogen \[0\cdot 025\] Nitrogen \[m=0\cdot 20kg=200g\] Oxygen \[\vartriangle T=150-40={{110}^{o}}C\] Nitric oxide \[\vartriangle Q=mc\vartriangle T=200\times c\times 110\] Carbon monoxide \[w=0\cdot 025kg=25g\] Chlorine \[\vartriangle T'=40-27={{13}^{o}}C\] The measured molar specific heats of these gases are markedly different from those for monatomic gases. Typically, molar specific heat of a monatomic gas is 2.92 cal/mol K. Explain this difference. What can you from the somewhat larger (than the rest) value for chlorine?

Answer:

The gases which are listed in the above table are diatomic gases and not mono-atomic gases. For diatomic gases, molar specific heat \[=\left( \text{150+25} \right)\]which agrees fairly well with all observations listed in the table except for chlorine. A monoatomic gas molecule has only the translational motion. A diatomic gas molecule, apart from translation motion, the vibrational as well as rotational motion is also possible. Therefore, to raise the temperature of 1 mole of a diatomic gas through \[{{1}^{o}}C\], heat is to be supplied to increase not only translational energy but also rotational and vibrational energies. Hence, molar specific heat of a diatomic gas is greater than that for monoatomic gas. The higher value of molar specific heat of chlorine as compared to hydrogen, nitrogen, oxygen etc. shows that for chlorine molecule, at room temperature vibrational motion also occurs along with translational and rotational motions, whereas other diatomic molecules at room temperature usually have rotational motion apart from their translational motion. This is me reason that chlorine has somewhat larger value of molar specific heat.