Select the statements below that are false and think about why they are not true.?

by definition

..ΔG = ΔH - TΔS

if ΔG < 0, the rxn is spontaneous

meaning

.. as long as ΔH < TΔS

the rxn is spontaneous

*********

now let's look at the wording of

.. ΔS(sys) vs ΔS(surr)

we can interpret that as

.. ΔS reaction vs ΔS surroundings

Assuming the surroundings is huge (the size of the universe) vs the system (our reactor) the temperature of the surroundings isn't going to change much as heat (dH) is transferred into or out of our "system" from or to the surroundings. right?  so the surroundings will be at constant temperature.  If it helps, imagine lighting a match.  Do you think that will change the temperature of the entire universe much?  Not at all right?

at constant temperature

.. ΔS = Q / T

i.e

.. ΔS(surr) = ΔH / T

and we just need to figure out the sign of ΔH

**********

let's look at the possible choices. 

*** A ***

this is FALSE.. because as long as TΔS(sys) > ΔH(sys) the reaction will be spontaneous. 

example

.. let ΔH = -1000 J/mol

.. .. .ΔS = - 3 J/molK

.. . ..T = 300k

.. ΔG = -1000 J/mol + -900 J/mol = -100 J/mol

and the rxn is spontaneous 

and ΔS < 0

*** B ***

this one's tricky... let's consider these 3 cases

.. ΔH(sys) < 0, 0 > ΔS(sys) > ΔH(sys)

.. ΔH(sys) < 0,  ΔS(sys) > 0 > ΔH(sys)

.. ΔH(sys) > 0, ΔS(sys) > ΔH(sys) > 0

where ΔG is negative... note that T is always positive

examples of each.. SYSTEM.. units are J/mol, J/molK and K

.. case 1... dH = - 1000, dS = -3, T = 300

.. case 2... dH = - 1000, dS = +3, T = 300

.. case 3... dH = +1000, dS = +3, T= 400

now the dH(surr) of each

.. case 1... dH sys is -, so dH surroundings is +

.. case 2... dH sys is -, so dH surroundings is +

.. case 3... dH sys is +, so dH surroundings is -

if you have trouble with this recall that heat flowing OUT

of a chemical reaction is defined as NEGATIVE.  Example, 

the combustion of gasoline releases heat.  So the dH of 

combustion of gasoline < 0 by convention.  That heat must go

into the surroundings.  So the surroundings have heat ADDED

to them.  And the sign of heat is then +.

now the dS(surr).. when dS(surr) = Q(surr) / T

.. case 1.. dS = +(1000 J/mol) / 300K) = + #

.. case 2.. dS = +(1000 J/mol) / 300K) = + #

.. case 3.. dS = -(1000 J/mol) / 300K) = - #

back to the question

.. True or False

.. IF dS(sys) is -, AND dG < 0, then dS(surr) > 0

we can see from case 1 and 2, when dS < 0, then dH(sys) < 0

and dH surroundings > 0..  Which means dS(surroundings) > 0

This is TRUE.

*** C ***

this is FALSE.

Again, wording is critical. 

Think conservation of energy.  if change change in a system (dG) is -, then the energy change of the surroundings must be + for conservation of energy to occur.

but the question asks for energy change of the UNIVERSE which includes system + surroundings. That is zero.

*** D ***

this is FALSE. 

dG = dH - TdS

for many many many reactions, increasing T decreases dG until dG < 0 and the rxn is spontaneous.