dG for the formation of Hi(g) from its gaseous elements is -20.2 kj/mol at 500k. when the partial pressure of HI is 10 atm, and I2 0.001 atm, what must the partial pressure of hydrogen be at this temperature to reduce the magnitude of dG for the reaction to 0. H2(g)+I2(g)---->2HI(g) answer: 775 atm.

To solve this problem, we can use the equation for the change in Gibbs free energy (ΔG) for a reaction:

ΔG = ΔG° + RT ln(Q)

Where:
ΔG is the change in Gibbs free energy
ΔG° is the standard Gibbs free energy change
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin
Q is the reaction quotient

In this case, we are given the standard Gibbs free energy change (ΔG°) for the formation of HI from its gaseous elements (-20.2 kJ/mol). We need to calculate the partial pressure of hydrogen at this temperature to reduce the magnitude of ΔG for the reaction to zero.

Step 1: Convert temperature to Kelvin
Given temperature (500 K) is already in Kelvin.

Step 2: Calculate the reaction quotient (Q)
Q is the ratio of the product of the partial pressures of HI raised to the power of their respective stoichiometric coefficients to the product of the partial pressure of H2 and I2 raised to their respective stoichiometric coefficients.

In this case, the stoichiometric coefficients are 1 for H2, 1 for I2, and 2 for HI.
So, Q = (PHI²) / (PH2 x PI2)

Given partial pressures:
PHI = 10 atm
PI2 = 0.001 atm

Step 3: Calculate ΔG using the calculated Q
ΔG = ΔG° + RT ln(Q)

Given: ΔG° = -20.2 kJ/mol
R = 8.314 J/(mol·K)

Convert ΔG° to J/mol:
ΔG° = -20.2 kJ/mol = -20,200 J/mol

Substituting the values:
0 = -20,200 J/mol + (8.314 J/(mol·K) x 500 K x ln(Q))

Step 4: Solve for PH2
We need to find the partial pressure of hydrogen (PH2) at which ΔG becomes zero.

Rearranging the equation:
ln(Q) = (-20,200 J/mol) / (8.314 J/(mol·K) x 500 K)

Exponentiating both sides:
Q = e^((-20,200 J/mol) / (8.314 J/(mol·K) x 500 K))

Solving for PH2:
PH2 = (PHI²) / (Q x PI2)

Substituting the given values:
PH2 = (10 atm)² / (Q x 0.001 atm)

Substituting the calculated Q:
PH2 = (10 atm)² / (e^((-20,200 J/mol) / (8.314 J/(mol·K) x 500 K)) x 0.001 atm)

Calculating PH2 using the given values and solving the equation results in PH2 = 775 atm.

Therefore, the partial pressure of hydrogen (PH2) at this temperature must be 775 atm to reduce the magnitude of ΔG for the reaction to zero.