# Physical Chemistry

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In this experiment, the degree of dissociation (a) of N2O4 into NO2 was studied using density and the ideal gas equation by regularly varying temperatures and taking corresponding readings. The equilibrium constant, Kp, was computed using a and the results were extended to find the values of enthalpy (?H), free energy (?G) and entropy (?S) of dissociation. The experimental values were found to be: ?H = 57.2 ± 1.38 kJ/mol, ?G = 5.7 ± 1.28 kJ/mol, and ?S = 172.9 ± 4.11 J/deg-mol. A comparison of the literature and experimental values is presented in this report in a table under the heading “Discussion.”

Introduction

The purpose of this experiment is to find the enthalpy, ?H, free energy, ?G, and entropy ?S of N2O4. These values are derived by finding the degree of dissociation (a) and equilibrium constant (Kp) of N2O4 by measuring the density of the gas at a known pressure and measuring the weight of the gas at constant pressure at different temperatures. The following equations, taken directly from the lab manual, were employed to find the required values.

a = PMV/WRT -1, KP = 4a2P/(1-a2)

where,

M = mol wt of undissociated N2O4,

P = the corrected barometric reading in atmospheres,

V = volume of bulb,

W = weight of gas in the bulb,

R = gas constant,

T = temperature in degrees Kelvin.

The equilibrium equation is,

N2O4 ? 2 NO2

If the value of Kp is > 1, then the reaction moves towards the products, if it is <1, the reaction favors the reactants.

Once Kp is found for all the separate trials, a plot can be made of ln (Kp) against 1/T. This gives us the value of Kp at 298 K. All the required values were found using this result in the following way:

?G = -RT ln (KP) where R is the gas constant

?H= – ?H/R where –R (slope of the plot of ln (Kp) vs. 1/T

?S = (?H – ?G)/T where T is the temperature in Kelvin

Procedure

The chemicals used in this process were 99.5% N2O4/NO2 gas mixture. To obtain the data regarding the dissociation of N2O4 into NO2, a vacuum setup was used, a Dumas bulb to contain the gas and a vacuum trap to prevent any gas from going into the pump and to protect the system from outside contaminants along with a manometer to monitor the pressure.

The bulb was first cooled in ice bath until the liquid started condensing. We immersed the bulb in water and stopcock opened until the gas disappeared. At varying temperatures, barometric pressure was read and the values were recorded.

Discussion

Derived values Value Error Literature value

?G°298K

(KJ/mol) 5.7 ±2.0 4.64

?H°298K (KJ/mol) 57.2 ±1.4 54

?S°298K (J/mol*K 172.9 ±6.0 172

Kc 25°C mol/L 4.89×10-4 – –

Literature values from National Bureau of Standards Technical Note 270-3, “Selected Values of Chemical Thermodynamic Properties,” pp. 61, 62

Apart from the slight difference in the literature and experimental values of ?H, the rest of the values are similar and the error is negligible. There are some safety concerns associated with the experiment. For example, NO2 is a strong oxidizer. The vapor pressure of NO2 is 0.96 bar at 20 degrees centigrade; there is always a chance of over-pressurizing the bulb. Our R^2 value of 0.9983 tells us that the data is quite accurate. Some air might have stayed in the bulb which could have affected the value for a which in turn would have increased the value of Kp and ?H.

The comprehensibility factor for N2O4 = 2 times the comprehensibility factor for NO2, because of two major reasons. The first factor that changed was the amount of moles, because of the larger molecular weight of N2O4 as compared to NO2. The second factor is that as Temperature increases, ‘Z’ of NO2 approaches 1 and equilibrium shifts to the right and when temperature decreases, ‘Z’ as N2O4 approaches 1 and the equilibrium shifts to the left

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**Category**: Mathematics