A reaction has delta G= +21.5 kj/mol, delta H= +25.0 kj/mol, and delta S= +15.0 j/mol*k can become spontaneous at a temperature of ? k.
The answer is 1670. How did they get that. What I did was isolate T and i got 233k. How would I go about answering this question.
I get 233 also if I plug in the numbers. What you have done is to solve for T for the conditions listed. What yo want to do is to set delta G = 0 (which is equilibrium point and anything negative is spontaneous).
0 = 25-T(0.015).
T = 1666 K which I would round to 1670 K.
Check my thinking.
To determine the temperature at which a reaction becomes spontaneous, you need to use the equation:
ΔG = ΔH - TΔS
Here, ΔG represents the change in Gibbs free energy of the reaction, ΔH is the change in enthalpy, ΔS is the change in entropy, and T is the temperature in Kelvin.
Given:
ΔG = +21.5 kJ/mol
ΔH = +25.0 kJ/mol
ΔS = +15.0 J/mol*K
To solve for T, you can rearrange the equation as follows:
TΔS = ΔH - ΔG
T = (ΔH - ΔG)/ΔS
Substituting the given values, you get:
T = (25.0 kJ/mol - 21.5 kJ/mol) / (15.0 J/mol*K)
Converting kJ to J and canceling out the units:
T = (25000 J/mol - 21500 J/mol) / 15.0 J/mol*K
T = 3500 J/mol / 15.0 J/mol*K
T = 233.33 K
It seems you made a calculation error in converting the kJ value to J. The correct temperature at which the reaction becomes spontaneous is approximately 233.33 K, which rounds to 233 K.
However, the correct answer given is 1670 K. It is possible that there was an error in the original question or the answer you received. Double-checking the values may help clarify any discrepancies.
To determine the temperature at which the reaction becomes spontaneous, we can use the equation:
ΔG = ΔH - TΔS
where:
ΔG is the change in Gibbs free energy,
ΔH is the change in enthalpy,
ΔS is the change in entropy, and
T is the temperature in Kelvin.
Given:
ΔG = +21.5 kJ/mol
ΔH = +25.0 kJ/mol
ΔS = +15.0 J/(mol*K)
First, we need to convert the units of ΔG, ΔH, and ΔS so that they are all in the same units (kJ/mol). Since ΔS is given in J/(mol*K), we need to divide it by 1000 to convert it to kJ/(mol*K):
ΔS = 15.0 J/(mol*K) = 0.015 kJ/(mol*K)
Now we can substitute the given values into the equation and solve for T:
ΔG = ΔH - TΔS
21.5 kJ/mol = 25.0 kJ/mol - T * 0.015 kJ/(mol*K)
Rearranging the equation and isolating T gives:
T = (25.0 kJ/mol - 21.5 kJ/mol) / (0.015 kJ/(mol*K))
T = 3.5 kJ/mol / 0.015 kJ/(mol*K)
T = 233.33 K
So, your calculation of T = 233 K is correct. However, the answer provided as 1670 K might be a rounding error. It is safer to use the exact value of 233.33 K.