Mole fraction The number of moles

Mole fraction The number of moles of a component of a mixture divided by the total number of moles in the mixture. 

For a system consisting of C components, the phase rule indicates that, in the two-phase region, there are F=C-2 + 2 = C degrees of freedom. That is, it takes C independent variables to define the thermodynamic state of the system. The independent variables may be selected from a total of 2C intensive variables (i.e., variables that do not relate to the size of the system) that characterize the system the temperature, pressure, C - 1 vapor-component mole fractions, and C - 1 liquid-component mole fractions. The number of degrees of freedom is the number of intensive variables minus the number of equations that relate them to each other. These are the C vapor-liquid equilibrium relations, Yj = K,X, i=l,. .., C. The equilibrium distribution coefficients, AT, are themselves functions of the temperature, pressure, and vapor and liquid compositions. The number of degrees of freedom is, thus, 2C - C = C, which is the same as that determined by the phase rule. 

We present here some experimental data on gas solubilities in liquids obtained in our laboratory. The liquid previously degassed is saturated by the unreacted gas, in a thermostated autoclave, provided with a mechanically bladed stirrer under a solute partial pressure p. After saturation attainment, a sample of the saturated liquid is taken via a syringe of high precision and injected into a gas-chromatograph in order to extract the solute dissolved in a known volume of the liquid sample V. By the way of calibration gas of known solute mole fraction, the number of... 

From the resulting mass increase of the individual tube filled with the suitable absorber, the mass of the individual gaseous products and their volume fraction (c, ) in the total volume of the gaseous products are calculated. On the basis of the volume fraction, the number of moles of the individual products ( 0 per 1 kg of propellant is calculated ... 

The solubility of hydrocarbon liquids from the same chemical family diminishes as the molecular weight increases. This effect is particularly sensitive thus in the paraffin series, the solubility expressed in mole fraction is divided by a factor of about five when the number of carbon atoms is increased by one. The result is that heavy paraffin solubilities are extremely small. The polynuclear aromatics have high solubilities in water which makes it difficult to eliminate them by steam stripping. 

Equation (A2.1.23) can be mtegrated by the following trick One keeps T, p, and all the chemical potentials p. constant and increases the number of moles n. of each species by an amount n. d where d is the same fractional increment for each. Obviously one is increasing the size of the system by a factor (1 + dQ, increasing all the extensive properties U, S, V, nl) by this factor and leaving the relative compositions (as measured by the mole fractions) and all other intensive properties unchanged. Therefore, d.S =. S d, V=V d, dn. = n. d, etc, and... 

Reflux ratio. This is defined as the ratio between the number of moles of vapour returned as refluxed liquid to the fractionating column and the number of moles of final product (collected as distillate), both per unit time. The reflux ratio should be varied according to the difficulty of fractionation, rather than be maintained constant a high efficiency of separation requires a liigh reflux ratio. ... 

The first and second columns of Table 1.4 give the number of moles of polymer in six different molecular weight fractions. Calculate and for this polymer and evaluate a using both Eqs. (1.7) and (1.18). 

For linear equiHbrium and operating lines, an expHcit expression for the number of theoretical plates required for reducing the solute mole fraction... 

For a PVnr system of uniform T and P containing N species and 7T phases at thermodynamic equiUbrium, the intensive state of the system is fully deterrnined by the values of T, P, and the (N — 1) independent mole fractions for each of the equiUbrium phases. The total number of these variables is then 2 + 7t N — 1). The independent equations defining or constraining the equiUbrium state are of three types equations 218 or 219 of phase-equiUbrium, N 7t — 1) in number equation 245 of chemical reaction equiUbrium, r in number and equations of special constraint, s in number. The total number of these equations is A(7t — 1) + r -H 5. The number of equations of reaction equiUbrium r is the number of independent chemical reactions, and may be deterrnined by a systematic procedure (6). Special constraints arise when conditions are imposed, such as forming the system from particular species, which allow one or more additional equations to be written connecting the phase-rule variables (6). 

For each stage J, the following 2C -1- 3 component material-balance (M), phase-equilibrium (E), mole-fraction-summation (S), and energy-balance (H) equations apply, where C is the number of chemical species ... 

This case includes most liquid reactions and also those gas reactions that operate at both constant temperature and pressure with no change in the number of moles during reaction. The relationship between concentration C and fractional conversion is as follows ... 

The partial pressure at a given pressure and temperature is lower when there are more moles of other components in the gas phase. The lower the partial pressure the greater the tendency of the component to flash to gas. Thus, the higher the fraction of light components in the inlet fluid to any separator, the lower the partial pressure of intermediate components in the gas phase of the separator, and the greater the number of intermediate component molecules that flash to gas. 

The term ff denotes the number of independent phase variables that should be specified in order to establish all of the intensive properties of each phase present. The phase variables refer to the intensive properties of the system such as temperature (T), pressure (P), composition of the mixture (e.g., mole fractions, x ), etc. As an example, consider the triple point of water at which all three phases—ice, liquid water, and water vapor—coexist in equilibrium. According to the phase rule,... 

The oxidation described here was performed in 80% (v/v) acetonitrile — 20 % water (mole fraction of water = 0.42) at 35.0 °C. Figure 2 shows the selectivity as a function of the number of carbon atoms in R2. In the case of oxidation of la and 2a (R2 = branched alkyl groups), the selectivity reaches a sharp maximum (r = 2.4) at the isopentyl group (j = 2)l8). For R2 = straight-chain alkyl groups, alternation in the selectivity is clearly observed 18). The difference between the r value for la and 2a2 and that for la and 2h2 reaches up to 3.7. 

Strategy First, calculate the number of moles of each gas (remember that oxygen is in excess). Then determine the mole fractions and finally the partial pressures. 

Strategy Start with a fixed mass of solution such as one hundred grams. First calculate the masses of H20 and H202, then the number of moles, and finally the mole fraction of H202. 

Strategy First (1), calculate the number of moles of glucose (MM = 180.16 g/mol) and water (MM = 18.02 g/mol). That information allows you to find (2) the mole fraction of glucose. Finally (3), use Raoult s law to find the vapor pressure lowering. 

Molarity (M) A concentration unit defined to be the number of moles of solute per liter of solution, 95q, 259 concentration unit conversion, 261-262 potassium chromate, 263 Mole A collection of6.0122 X 1023 items. The mass in grams of one mole of a substance is numerically equal to its formula mass, 55. See also Amount Mole fraction (X) A concentration unit defined as the number of moles of a component divided by the total number of moles, 116-117,261 Mole-gram conversions, 55-56,68-68q... 

---