There is not enough information to calculate ΔGrxn because the amount of pressure for the reactant and the product are not given. These are needed in order to satisfy the following equation:
ΔGrxn = ΔG°rxn + RTlnQ, where ΔGrxn is Gibb's free energy in a specific condition, ΔG°rxn is Gibb's free energy in standard conditions (pressure equals to 1 atm for each gas component), R is 8.314 J/(mol*K), T is temperature in Kelvin, and Q is the rate constant. Q is determined by knowing the amount of pressure of all the gas components in the reaction.
Despite this problem, ΔG°rxn is determined by looking at values from a source. I'll show you how to solve this problem when the problem is asking for ΔG°rxn because ΔG°rxn is different from ΔGrxn. I posted a website with values of ΔH° and ΔS° to satisfy the equation:
ΔG°rxn = ΔH° - TΔS°
ΔH° is calculated by subtracting the standard enthalpy of N2O4 from two times the standard enthalpy of NO2.
ΔH° = 2(H° of NO2) - (H° of N2O4) = 2(33.1 kJ/mol) - 9.08 kJ/mol = 57.12 kJ/mol
ΔS° is calculated by subtracting the standard entropy of N2O4 from two times the standard entropy of NO2.
ΔS° = 2(S° of NO2) - (S° of N2O4) = 2(240.04 J/(mol*K)) - 304.38 J/(mol*K) = 175.7 J/(mol*K)
Before these values are inserted to obtain a value for ΔG°rxn, all of the values should have kJ because ΔG°rxn normally has the units kJ/mol; therefore, ΔS° should be converted.
Assuming you advise 5.50 x 10^-2 M: let the quantity of N2O4 that decomposes be x. Then [NO2] = 2x and the perfect [N2O4] = (5.50 x 10^-2) - x. [NO2]^2/[N2O4] = (x^2)/(5.50x10^-2 - x) = 0.513 x^2 = (2.82x10^-2) - 0.513x And from there you should apply the quadratic formulation to unravel for x.
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There is not enough information to calculate ΔGrxn because the amount of pressure for the reactant and the product are not given. These are needed in order to satisfy the following equation:
ΔGrxn = ΔG°rxn + RTlnQ, where ΔGrxn is Gibb's free energy in a specific condition, ΔG°rxn is Gibb's free energy in standard conditions (pressure equals to 1 atm for each gas component), R is 8.314 J/(mol*K), T is temperature in Kelvin, and Q is the rate constant. Q is determined by knowing the amount of pressure of all the gas components in the reaction.
Despite this problem, ΔG°rxn is determined by looking at values from a source. I'll show you how to solve this problem when the problem is asking for ΔG°rxn because ΔG°rxn is different from ΔGrxn. I posted a website with values of ΔH° and ΔS° to satisfy the equation:
ΔG°rxn = ΔH° - TΔS°
ΔH° is calculated by subtracting the standard enthalpy of N2O4 from two times the standard enthalpy of NO2.
ΔH° = 2(H° of NO2) - (H° of N2O4) = 2(33.1 kJ/mol) - 9.08 kJ/mol = 57.12 kJ/mol
ΔS° is calculated by subtracting the standard entropy of N2O4 from two times the standard entropy of NO2.
ΔS° = 2(S° of NO2) - (S° of N2O4) = 2(240.04 J/(mol*K)) - 304.38 J/(mol*K) = 175.7 J/(mol*K)
Before these values are inserted to obtain a value for ΔG°rxn, all of the values should have kJ because ΔG°rxn normally has the units kJ/mol; therefore, ΔS° should be converted.
ΔS° = 175.7 J/(mol*K)*1kJ/1000J = 0.1757 kJ/(mol*K)
These known values and the given temperature should be plugged into the following equation to receive a value for ΔG°rxn.
ΔG°rxn = ΔH° - TΔS° = 57.12 kJ/mol - 400K*0.1757 kJ/(mol*K) = -13.16 kJ/mol
Hope this helps.
Assuming you advise 5.50 x 10^-2 M: let the quantity of N2O4 that decomposes be x. Then [NO2] = 2x and the perfect [N2O4] = (5.50 x 10^-2) - x. [NO2]^2/[N2O4] = (x^2)/(5.50x10^-2 - x) = 0.513 x^2 = (2.82x10^-2) - 0.513x And from there you should apply the quadratic formulation to unravel for x.