Calculate the standard free energy change for the below reaction at 25 degrees Celsius?

#CH_4"(g)"+2O_2"(g)"\toCO_2"(g)"+2H_2O"(l)"#


#\DeltaG_{f,H_2O"(g)"}^{o}=-237.2"kJ"/"mol"#
#\DeltaG_{f,CO_2"(g)"}^{o}=-394.4"kJ"/"mol"#
#\DeltaG_{f,CH_4"(g)"}^{o}=-50.8"kJ"/"mol"#

Answer 1

I'll assume these are all gases (in a coffee-cup calorimeter), although water liquid is possible in a bomb calorimeter. As a note, you should be especially careful that the values you look at are correct.

Here I get #DeltaG_(rxn)^@ = -"818 kJ"# per mol of methane.

Two things that can give you trouble are:

Due to the fact that the Gibbs' free energy #G# is a state function, we can write:
#DeltaG_(rxn)^@ = sum_P n_P DeltaG_(f,P)^@ - sum_R n_RDeltaG_(f,R)^@#
where #DeltaG_f^@# is the change in Gibbs' free energy of reaction at #25^@ "C"# and #"1 atm"# in #"kJ/mol"#, and #P# and #R# are products and reactants. #n# is the mols of substance.

So, you take the sum over the products, sum over the reactants, and subtract the sums, making sure you get the phases correct, and the coefficients match up.

Also, the #DeltaG_f^@# for elements in their standard state is ZERO. If you are not given the value, it is a good sign that you already know it "by heart".

Important standard state examples are:

#"H"_2(g), "C"(grap hite), "Al"(s), "P"_4(s), "S"_8(s)#

(if you care, sulfur is actually orthorhombic in its standard state.) You should however definitely know that carbon graphite is the standard state of carbon, not diamond.)

The main diatomics to know here are #"H"_2(g)#, #"O"_2(g)#, #"F"_2(g)#, #"Br"_2(l)#, #"I"_2(s)#, #"N"_2(g)#, and #"Cl"_2(g)#. The rest should be fairly predictable, like #"Mn"(s)# and #"Pb"(s)#.

Therefore, for

#"CH"_4(g) + 2"O"_2(g) -> "CO"_2(g) + 2"H"_2"O"(g)#

we just have:

#color(blue)(DeltaG_(rxn)^@) = ["1 mol" cdot DeltaG_(f,CO_2(g))^@ + "2 mols" cdot DeltaG_(f,H_2O(g))^@] - ["1 mol" cdot DeltaG_(f,CH_4(g))^@ + "2 mols" cdot "0 kJ/mol O"_2(g)]#
#= ["1 mol" cdot -"394.4 kJ/mol CO"_2(g) + "2 mols" cdot -"237.2 kJ/mol H"_2"O"(g)] - ["1 mol" cdot -"50.8 kJ/mol CH"_4(g) + "2 mols" cdot "0 kJ/mol O"_2(g)]#
#=# #color(blue)(-"818 kJ")#
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Answer 2

To calculate the standard free energy change (ΔG\Delta G^\circ) for a reaction at 25 degrees Celsius, you can use the equation:

ΔG=ΔHTΔS\Delta G^\circ = \Delta H^\circ - T \cdot \Delta S^\circ

Where:

  • ΔH\Delta H^\circ is the standard enthalpy change
  • ΔS\Delta S^\circ is the standard entropy change
  • TT is the temperature in Kelvin

Without the reaction provided, it's not possible to calculate the standard free energy change. If you provide the reaction along with the standard enthalpy change (ΔH\Delta H^\circ) and the standard entropy change (ΔS\Delta S^\circ), I can assist you with the calculation.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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