Nitrogen dioxide, a pollutant in the atmosphere, can combine with water to from nitric acid. One of the possible reactions is shown below. Calculate ∆G0 and Kp for this reaction at 25oC and comment of on the spontaneity of the reaction (MUST plot the data and find enthalpy and entropy changes and then calculate free energy change):
3NO2(g) + H2O(l)2HNO3(aq) + NO(g). Temperature
150 K Kp 1.4x10-6
175 K Kp 4.6x10-4
200 K Kp 3.6x10-2
225 K Kp 1.1
250 K Kp 15.5
Dry ice freezes at -79 °C. What is this temperature in °F? ….in K?
To calculate the ∆G0 and Kp for the reaction, we need to use the van 't Hoff equation, which relates the equilibrium constant Kp to the standard Gibbs free energy change ∆G0:
∆G0 = -RT ln(Kp)
Where:
∆G0 is the standard Gibbs free energy change
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin
Kp is the equilibrium constant expressed in terms of partial pressures
To use the van 't Hoff equation, we first need to determine the enthalpy change (∆H) and entropy change (∆S) for the reaction. This can be done by analyzing the given data and finding the slope and intercept of the plot of ln(Kp) vs. 1/T.
We can start by writing down the given data and converting the temperatures to Kelvin:
Temperature (K) Kp
150 1.4x10^(-6)
175 4.6x10^(-4)
200 3.6x10^(-2)
225 1.1
250 15.5
Next, we can plot ln(Kp) against 1/T:
ln(Kp) vs. 1/T
ln(1.4x10^(-6)) vs. 1/150
ln(4.6x10^(-4)) vs. 1/175
ln(3.6x10^(-2)) vs. 1/200
ln(1.1) vs. 1/225
ln(15.5) vs. 1/250
Now, we can find the slope (m) and intercept (b) of the best-fit line through these points.
By analyzing the plot, we can determine that the slope of the line, m, represents ∆H/R, and the intercept, b, represents ∆S/R.
Using the slope and intercept, we can calculate ∆H and ∆S:
∆H/R = m
∆S/R = b
Once we have determined ∆H and ∆S, we can substitute these values into the van 't Hoff equation to calculate ∆G0 at 25°C (298 K) and comment on the spontaneity of the reaction.