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1.
Although heat is path function but heats absorbed by the system under certain specific conditions is independent of path. what are those conditions? Explain when volume remains constant.
2.
18.0 g water completely vaporises at 100 oC and 1 bar pressure and the enthalpy change in the process is 40.79 KJ mol-1. What will be the enthalpy change for vaporising two moles of water under the same conditions? What is the standard enthalpy of vaporisation for water?
3.
Expansion of a gas in vacuum is called free expansion. Calculate the work done and the change in internal energy when 1L of ideal gas expands isothermally into vacuum until its total volume is 5 L?
4.
An ideal gas is allowed to expand against a constant pressure of 2 bar from 10 L to 50 L in one step. Calculate the amount of work done by the gas. If the same expansion were carried out reversibly, will the work done be higher or lower than the earlier case (given that 1 L bar = 100 J)?
5.
The enthalpy of a vaporisation of CCI4 is 30.5 kJ mol-1. Calculate the heat required for the vaporisation of 284g of CCI4 at constant pressure (molar mass of CCI4 =154 g mol-1)
1.
At Constant volume By first law of thermodynamics, \(\triangle U=q+W \ or \ q=\triangle U-W.\)But \(W=-p\triangle V.\) Hence, \(q=\triangle U+p\triangle V.\) But as volume remains constant, \(\triangle V=0\) .
\(\therefore qV=\triangle U\). But \(\triangle U\) is state function. Hence, \(q_{ v }\) is state function.
2.
18.0 g H2O = 1 mol H2O
Enthalpy change for vaporising 1 mole of H2O = 40.79 KJ
\(\therefore \) Enthalpy change for vaporising 2 moles of
H2O = 2 x 40.79 KJ = 81.58 KJ
Standard enthalpy of vaporisation at 100oC and 1 bar pressure,
\({ \triangle }_{ vap }{ H }^{ \circ }=+40.79 \ KJ \ { mol }^{ -1 }\)
3.
\(Work \ done,\ W=-{ p }_{ ext }({ V }_{ 2 }-{ V }_{ 1 })\)
\(As \ { p }_{ ext }=0,\ so \ w=-0(5-1)=0\)
\( For \ isothermal \ expansion,\)
\( \triangle U=0 \ as \ \triangle T=0\)
4.
In the first case, as the expansion is against constant external pressure,
\(w=-{ p }_{ ext }({ V }_{ 2 }-{ V }_{ 1 })\)
\( =-2bar\times (50-10)L\)
\( =-80Lbar=-80\times 100J\)
\( =-8kJ\)
If the above expansion were carried out reversibly, the internal pressure of the gas should be infinitesimally greater that external pressure at every stage. Hence, the work done will be more.
5.
1 mole of CCI4 = 154 g
Heat required for vapourising 154 g CCI4 = 30.5 kJ
\(\therefore\) Heat required for vapourising
\(284 \ g \ CC{ I }_{ 4 }=\frac { 30.5\times 284 }{ 154 } kJ=56.25kJ\)
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