Chemical Engineering Principles: Definitions and Calculations

Differentiate Between Unit Process and Unit Operation

Unit Operation: A physical step in a process that involves a physical change (e.g., distillation, filtration, drying, crushing). It deals with the principles of momentum, heat, and mass transfer.

Unit Process: A chemical step in a process that involves a chemical change or reaction (e.g., nitration, hydrogenation, polymerization). It deals with the chemical transformation of materials.

Define Orsat Analysis

Orsat analysis is a wet chemical method for the volumetric analysis of flue gases or other gas mixtures. It specifically measures the percentages (by volume) of carbon dioxide ($\text{CO}_2$), oxygen ($\text{O}_2$), and carbon monoxide ($\text{CO}$). The remaining gas is assumed to be nitrogen ($\text{N}_2$).

State Amagat’s Law of Additive Volumes

Amagat’s Law states that the total volume of a gas mixture, at constant temperature and pressure, is equal to the sum of the partial volumes that each gas would occupy if it existed alone at the same temperature and pressure.

Formula: $V_{\text{total}} = V_A + V_B + V_C + \dots$ at constant $T$ & $P$.

Significant Figures Rule for Addition or Subtraction

The result should have no more decimal places than the measurement with the least number of decimal places.

Define Recycle Ratio

The recycle ratio is the ratio of the quantity (mass or molar flow rate) of a stream recycled back to the process entrance to the quantity of the fresh feed stream.

Wet Bulb Depression

Wet Bulb Depression is the difference in temperature between the dry-bulb temperature (the normal air temperature) and the wet-bulb temperature (the lowest temperature to which air can be cooled by evaporating water into it).

Relative Humidity vs. Percent Humidity

• Relative Humidity (RH): The ratio of the partial pressure of water vapor in the air to the vapor pressure of water at the system temperature, expressed as a percentage. $R_h = (p_w / p_w^*) \times 100\%$.
• Percent (or Percentage) Humidity: The ratio of the actual mass of water vapor in a unit mass of dry air to the mass of water vapor the same mass of dry air would hold if saturated at the same temperature, expressed as a percentage.

Extent of Reaction and Limiting Reactant Identification

The extent of reaction ($\xi$) is defined for the reaction $aA + bB \rightarrow cC + dD$ as $\xi = \frac{n_i – n_{i0}}{\nu_i}$, where $\nu_i$ is the stoichiometric coefficient (negative for reactants).

For each reactant, calculate the maximum possible extent of reaction ($\xi_{\text{max}}$) if that reactant were to be completely consumed.

Theoretical Flame Temperature

The theoretical or adiabatic flame temperature is the maximum possible temperature achieved when a fuel is burned completely with a given amount of air or oxygen under adiabatic conditions (i.e., no heat loss to the surroundings and no work extraction).

Evaluation of Absolute Humidity

Absolute Humidity (also called humidity ratio) is the mass of water vapor present per unit mass of dry air.

Description of an Unsteady-State, Closed System

Definition: An unsteady-state (or transient) closed system is a thermodynamic system where:

1. No mass is allowed to cross its boundary (closed system / control mass).
2. The thermodynamic properties (e.g., pressure, temperature, internal energy) within the system change with time due to an interaction with its surroundings in the form of heat or work transfer.

Example: Heating Air in a Rigid, Sealed Tank. A perfect illustration is a rigid, sealed tank containing a fixed mass of air, which is then heated by an external source.

Calculating Heat of Reaction at Temperature T

To calculate the heat of reaction at a temperature $T$ when the standard heat of reaction $\Delta H^{\circ}_{\text{rxn}}(T_0)$ at a reference temperature $T_0$ (usually 298 K) is known, Kirchhoff’s Law is applied. This law utilizes the temperature dependence of enthalpy and the heat capacities of the reactants and products.