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This problem has to calculate equilibrium conversion at high temperature and low pressure.
The feed has both steam and C4H8, which is butene. The reason for the stream is to keep
the catalyst clean from the carbon deposits. Steam then also affects the equilibrium conversion.
So first step is calculating the equilibrium conversion, and we will start with our general
equation and then simplify. Write the fugacities raised to there stoichiometric coefficients,
and it is the products of these fugacities, and because of the low pressure and the high
temperature. We cab assume ideal gasses. So I should have written this more general. This
is really the fugacity divided by the standard state fugacity. The ideal gas, we are going
to set the fugacity of each of the components equal to its partial pressure and then our
standards states are 1 bar. So that this term will disappear or equilibrium constant is
going to be the products of our pressures at equilibrium raised to their stoichiometric
coefficients. So this means that pressure of hydrogen, the pressure of C4H6, the pressure
of C4H8, and the stoichiometric coefficients, and in our original equation, are 1 in each
case. So therefore each of our stoichiometric coefficients are 1. So we can write this in
terms of mole fractions. Mole fraction of hydrogen times pressure, the mole fraction
of C4H6 times pressure, and the mole fraction of the butene times pressure, and so just
simplified the equation for the equilibrium constant, and we know to value the equilibrium
constant. So we know to use the reaction equation. Again we started out with, lets say 1 mole
of C4H8, and in the inlet 0 moles of these, and for the x number of moles reacting right.
So it this would be the start. This would be at equilibrium. So the total moles is 1
mole of C4H8, and 10 moles of stream. Now in the equilibrium calculation we want the
mole fractions. So I am going to; the mole fraction of hydrogen is x over 11 plus x,
and 11 plus x is the total number of moles at equilibrium. So we start off with 1 moles
here. 1 at the start. Afterwards we have 10 moles of stream plus 1-x miles of c4h8, x
moles of C4H6, x moles of hydrogen. So this number also turned out to be the mole fraction
of course of C4H6, and the mole fraction of C4H8 is 1 minus x over 11 plus x. So now we
are ready to go back and substitute into the equation in terms of mole fractions. We have
the equilibrium constant, which is 0.3299. The pressure is 1, the mole fractions of hydrogen
and C4H6 are both 11 plus x in the numerator, and mole fraction of C4H8 in the denominator,
and so this simplifies a bit. We can solve this equation to find x and x is 0.825. So
this means that 82.5 percent of butene is converted at equilibrium. So part B says what
happens of there is no steam. Well the main thing it changes is the total number of moles.
It is now just 1 plus x instead of the 11 plus x. Our equilibrium expression other wises
is the same. x squared, 1 minus x, and now instead of 11 it is just 1 plus x. Now x is
0.498. So now we have 50 percent converted without steam. So the steam increase the conversion,
and this is because we have a gas phase reaction. So if we look at our reaction 1 mole of gas
forms 2 moles of gas, and we are essentially lowering the pressure by adding the steam,
since total pressure is constant, that pushes the reaction to the right by Le chatelier's
principle. Then it checks we expect a lower conversion because of this, and that is what
we calculate.