okay let's look at a problem regarding free energy and non-standard conditions
consider the following reaction and the non-standard conditions below so we have
two NH3 yielding three H2 plus N2 and we have the standard free energy change as
being equal to 33.0 kilojoules per mole now here are the non-standard
conditions we were referring to we have a temperature of 25 degrees Celsius and
then we have some pressures for these three gases for ammonia that's twelve
point nine atmospheres for hydrogen that's zero point two five zero
atmospheres and for nitrogen that's zero point eight seven zero atmospheres now
we call these non-standard conditions because we are not at equilibrium we are
also not at standard temperature so the free energy change is not going to be
the standard free energy change it's going to have a different value because
the standard free energy change is calculated at standard conditions if we
are not under standard conditions we have a different Delta G value so we are
going to want to calculate that here what is the free energy change for this
process so that's all the data we need go ahead and give this a try.
so let's put our reaction up top and let's put all of our information right there so we
are going to need to use this equation we know that Delta G meaning the free
energy change of some process under some conditions that are not standard
conditions is going to be equal to the standard free energy change plus RT ln Q
where Q is the reaction quotient so let's plug in what we know we know that
the standard free energy change is 33.0 kilojoules per mole that was given to us
then for R that's the gas constant we are going to use the version of the gas
constant that is 8.314 joules per mole kay and in particular we are going to
want to convert this into kilojoules per mole K because we need it to agree with
the free energy change value so that's in kilojoules per mole so let's take
this and divide by a thousand that gives us zero point zero zero eight three one
four kilojoules per mole K then temperature as we said is 25 degrees
Celsius which as always we convert into Kelvin so that's 298 K now for Q that's
the reaction quotient so that is going to be equal to the concentrations of the
products raised to the powers of their stoichiometric coefficients divided by
the concentration of the reactants raised to the powers of their
stoichiometric coefficients so here rather than concentrations we can just
use pressures and so let's take the pressure of H2 which is zero point two
five zero and let's raise it to the third power
because we have three H2 and let's multiply by the value for N2 which is
zero point eight seven zero and then we will divide by the value for NH3 which
is twelve point nine and we will square that because we have two NH3 in the
equation and so if we do the arithmetic Q is going to be equal to eight point
one seven times ten to the negative five now to get Delta G let's first take our
standard free energy change value that's thirty three point zero and we'll
subtract from that RT ln Q so we can put that in the calculator all at once that
will come out to twenty three point three and that gives us a delta g value
of nine point seven kilojoules per mole.