Consider the reaction: N2+3H2→2NH3 carried out at constant temperature and pressure. If ΔH and ΔU are the enthalpy and internal energy changes for the reaction, which of the following expressions is true ?
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Solution
ΔH=ΔU+ΔnRT for N2+3H2→2NH3
Δng= 2 – 4= – 2
∴ΔH=ΔU 2RT or ΔU=ΔH+2RT ∴ΔU>ΔH
An ideal gas expands in volume from 1 × 10-3 to 1 × 10-2 m3 at 300 K against a constant pressure of 1×105Nm-2. The work done is
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Solution
W=-PΔV=-10(1×10-2-1×10-3)=-900J
Which of the following is combustion reaction?
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Solution
Combustion is heating of substance in excess of oxygen so as to form carbon bioxide and water.Sometimes water is not formed during combustion.
Assume each reaction is carried out in an open container.For which reaction will ΔH =ΔE ?
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Solution
We know that ΔH =ΔE + ΔngRT
In the reaction, H2(g) + Br2(g)→2HBr(g)
Δn = np – nr= 2– 2= 0
So, ΔH =ΔE for this reaction
The molar heat capacity of water at constant pressure is 75JK-1mol-1. When 1kJ of heat is supplied to 100 g of water,which is free to expand, the increase in temperature of water is
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Solution
Given CP = 75 JK-1 mol-1
n=100⁄18mole,Q = 1000 J ΔT = ?
Q =nCPΔT ⇒ΔT=\(\frac{1000\times 18}{100\times 75}=2.4 K\)
The work done during the expansion of a gas from a volume of 4 dm3 to 6 dm3 against a constant external pressure of 3 atm is(1 L atm =101.32 J)
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Solution
W = – pΔV=-3(6-4)=-6 litre atmosphere
=-6×101.32=-608J
For the reaction
C3H8(g)+5O2(g)→3CO2(g)+4H2O(l)
at constant temperature, ΔH –ΔE is
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Solution
ΔH=ΔE+nRT
Δn = 3 – (1 + 5)= 3 – 6 = –3
ΔH-ΔE=(-3RT)
The heat of combustion of methane at 298° K is expressed by
CH4(g)+2O2(g)→CO2(g)+2H2OandΔH= 890.2
kJ. Magnitude of ΔE of reaction at this temperature is
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Solution
CH4(g)+2O2(g)→CO2(g)+2H2O
ΔH = 890 kJ (given)
By Ist law of thermodynamics
ΔH = ΔE +ΔnRTT
Where,
ΔH = change in enthalpy of reaction
ΔE = change in internal energy of reaction
Δn = change in number of gaseous moles.
= (nPnR)
According to question,
⇒ΔE = ΔH –ΔnRT= ΔH – (1 – 3)RT
= ΔH + 2RT = 890 + 2RT
Hence ΔE > ΔH
Option (d) is correct
In a closed insulated container, a liquid is stirred with apaddle to increase the temperature, which of the following is true?
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Solution
Internal energy is dependent upon temperature andaccording to first law of thermodynamics total energy ofan isolated system remains same, i.e., in a system ofconstant mass, energy can neither be created nordestroyed by any physical or chemical change but canbe transformed from oneform to another
ΔE=W≠0,0=q
For closed insulated container, q= 0, so, ΔE = + W, aswork is done by the system
One mole of anideal gas at 300 K is expanded isothermally from aninitial volume of 1 litre to 10 litres. The ΔE for this process is (R =2 cal. mol-1 K-1)
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Solution
For an isothermal process ΔE = 0