Question

I need help for my Pchem lab!!

Exercise 2. "Orthobaric densities" This exercise can be completed in either Excel (you can use your Excel file from Example 1 as a template), Graphical Analysis, or Mathematica. Note: If you decide to use Mathematica to create plots, make sure to label all axes, adjust plot ranges, and include plot legends as described in this handout. Introduction. The orthobaric density of a compound is the density of coexisting phases (liquid, gas, or solid) at a given temperature [122]. For any temperature below the critical point (CP), the density of the gas will be less than that of the liquid [22]. At the critical point, the density of the liquid and gas phases are identical, and the compound becomes a supercritical fluid [22]. It was shown 123] that densities of coexisting liquid and gaseous substance can be represented well by the empirical equation (46) (47) where Te is the critical temperature of the substance, pe is the substance density at critical temperature (Te) and critical pressure (pc), and a and b are empirical constants, specific for each P Pe+ a(Te -T)+b(Te T)13 substance. Recall that Te and pe are called the critical constants of a substance [17,18]. At and above the critical temperature Te, a single uniform phase called a supercritical fluid fills the container and an interface no longer exists [17,18]. That is, above the critical temperature, the liquid phase of the substance does not exist [17,18]. Figure 3. a) A liquid in equilibrium with its vapor. (b) When a liquid is heated in a sealed container, the density of the vapor phase increases and that of the liquid decreases slightly. There comes a stage, (c), at which the two densities are equal and the interface between the fluids disappears. This disappearance occurs at the critical temperature, Te [17,18]. la) b The critical temperature of oxygen, Te(02)-155 K, for instance, signifies that it is impossible to liquid oxygen by compression alone if its temperature is greater than 155 K: to liquefy n a fluid phase that does not occupy the entire volume - the temperature must oxygen-to obtai page 93 of 98

Answer 1

The observation table after data processing is

T (K)	Tc - T	(Tc-T)^1/3	den (liquid)	den (gas)	1/2*[den(liq)+den(liq)]	[den(liq)-den(liq)]
131	1.86	1.229809	0.43365	0.18462	0.309135	0.24903
130.7	2.16	1.292661	0.44026	0.17767	0.308965	0.26259
129.8	3.06	1.451801	0.4564	0.16357	0.309985	0.29283
128	4.86	1.693865	0.4919	0.13601	0.313955	0.35589
125.7	7.16	1.927396	0.52083	0.11607	0.31845	0.40476
121	11.86	2.280490	0.56582	0.08202	0.32392	0.4838
109.2	23.66	2.870813	0.65262	0.04014	0.34638	0.61248
107.8	25.06	2.926355	0.66168	0.03681	0.349245	0.62487
103.6	29.26	3.081471	0.6856	0.02824	0.35692	0.65736
101.6	31.26	3.150139	0.69953	0.02389	0.36171	0.67564
94.3	38.56	3.378410	0.73408	0.01422	0.37415	0.71986
90.4	42.46	3.488671	0.75446	0.01019	0.382325	0.74427
87.3	45.56	3.571587	0.76904	0.00774	0.38839	0.7613
82.4	50.46	3.695295	0.79086	0.00477	0.397815	0.78609
73.7	59.16	3.896512	0.82554	0.00171	0.413625	0.82383
68.3	64.56	4.011633	0.84714	0.0008	0.42397	0.84634

Graph for calculation of empirical constant b is as follows

Slope for this line is 0.217 and the relationship between two variables is $\rho_{l}-\rho_{g} = 2b (T_{c}-T)^{1/3}$

hence the slope is 2b = 0.217

b= 0.1085