Introduction to Chemical Engineering Calculations: Stoichiometry, Process Variables, and Concentration Expressions

Introduction to Chemical Engineering Calculations

Stoichiometry and Its Importance

Chemical engineering calculations, often referred to as stoichiometry, involve the use of chemical formulas and balanced chemical equations to interpret quantitative data. These calculations are essential for applying the laws of conservation of mass and energy in chemical processes.

• Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction.

• Applications include process design, optimization, and analysis in industrial chemical plants.

Processes and Process Variables

Key Process Variables

Process variables are measurable quantities that characterize the operation of chemical processes and individual units.

• Mass: The amount of matter in a system.

• Volume: The space occupied by a substance.

• Flow Rate: The quantity of material passing through a point per unit time.

• Chemical Composition: The identity and proportion of chemical species present.

• Pressure: The force exerted per unit area.

• Temperature: The measure of thermal energy within a system.

The Mole Concept

Definition and Significance

• The mole (n) is a fundamental SI unit for the amount of substance.

• One mole contains Avogadro's number of particles: $1\ \text{mol} = 6.022 \times 10^{23}$ particles (molecules, atoms, or ions).

Gram-Atom and Gram-Mole

• Gram-atom (g-atom): The amount of an element whose mass in grams equals its atomic weight.

• Gram-mole (g-mol): The amount of a compound whose mass in grams equals its molecular weight.

Key Equations

• For elements: $\text{Atomic weight (AW)} = \frac{\text{weight (wt)}}{\text{number of moles (n)}}$

• For compounds: $\text{Molecular weight (MW)} = \frac{\text{weight (wt)}}{\text{number of moles (n)}}$

Expressing Concentrations

Common Units and Formulas

Concentration Unit	Formula
Weight Percent (wt%)	$\text{wt\% of A} = \frac{\text{mass}_A}{\text{mass}_{\text{soln}}} \times 100$
Mole Percent (mol%)	$\text{mol\% of A} = \frac{n_A}{n_{\text{soln}}} \times 100$
Volume Percent (vol%)	$\text{vol\% of A} = \frac{V_A}{V_{\text{soln}}} \times 100$
Molarity (M)	$M = \frac{n_{\text{solute}}}{V_{\text{soln}} (L)}$
Molality (m)	$m = \frac{\text{moles solute}}{\text{mass solvent (kg)}}$
Parts per Million (ppm)	$\text{ppm} = \frac{\text{mass}_{\text{solute}}}{V_{\text{soln}} (L)}$

Density and Specific Gravity

Density ($\rho$)

• Density is the mass per unit volume of a substance.

• Formula: $\rho = \frac{m}{V}$ (in $\frac{g}{mL}$ or $\frac{kg}{m^3}$)

Specific Gravity (S.G. or G)

• Specific gravity is the ratio of the density of a substance to the density of a reference substance (usually water at 4°C).

• Formula: $\text{S.G.} = \frac{\rho_{\text{substance}}}{\rho_{\text{water}}}$

Hydrometer Scales

Scale	Formula
Degree Baumé ($^\circ$Bé)	$^\circ\text{Bé} = \frac{145}{\text{S.G.}} - 145$ (if S.G. > 1) $^\circ\text{Bé} = 140 - \frac{130}{\text{S.G.}}$ (if S.G. < 1)
Degree Twaddell ($^\circ$Tw)	$^\circ\text{Tw} = 200(\text{S.G.} - 1)$
Degree API ($^\circ$API)	$^\circ\text{API} = \frac{141.5}{\text{S.G.}} - 131.5$

Limiting and Excess Reactant

Definitions

• Limiting Reactant: The reactant that is completely consumed first in a chemical reaction, thus limiting the amount of product formed.

• Excess Reactant: The reactant that remains after the limiting reactant is fully consumed.

Degree of Completion

• Indicates how much of the limiting reactant is converted to product.

• Formula: $\text{Degree of Completion} = \frac{\text{Limiting Reactant converted to product}}{\text{Supplied Limiting Reactant}} \times 100\%$

Percent Excess Reactant

• Measures how much excess reactant remains, assuming a 100% complete reaction.

• Formula: $\%\ ER = \frac{\text{Supplied ER} - \text{Theoretical ER}}{\text{Theoretical ER}} \times 100\%$

Sample Problems

Sample Problem 1

Given 620 kg of dinitrogen pentoxide, calculate:

• g-mol dinitrogen pentoxide

• g-atom N

• g-mol O2

• kg Nitrogen

• grams of Oxygen

• grams of O2

• dinitrogen pentoxide molecules

• O atoms

• O2 molecules

Sample Problem 2

Given 1 tonne of a mixture of 60% malachite, Cu2CO3(OH)2, and 40% emerald green, Cu(C2H3O2)2·3CuAs2O4, calculate the mass of copper that can be obtained.

Sample Problem 3

A solution of MgCl2 has a molarity of 4.0 at 20°C. If its density at 20°C is 1.10 g/mL, report the composition in:

• Weight Percent

• Mole Percent

• Molality

• ppm of the Solute

Sample Problem 4

It is desired to prepare an aqueous solution containing 20% by weight Cobalt (II) chloride:

• How much Cobalt (II) chloride hexahydrate crystals must be added to 2.0 L of water?

• Calculate the volume of solution formed in m3/m3 of water.

• Find the composition of the solution in mol %, vol%, molarity, and molality.

Given: $\rho_{\text{water}} = 0.996\ \text{g/mL}$, $\rho_{\text{soln}} = 1.53\ \text{g/mL}$

Sample Problem 5

One of the ionic components of seawater is Mg2+ with a concentration of 0.129 by wt%. If the specific gravity of seawater is 1.03:

• What is the composition in ppm of Mg2+?

• How much MgCl2 could be recovered from a cubic meter of seawater?

Sample Problem 6

An oil has a specific gravity of 0.81. Calculate its gravity in degrees Baumé and degrees API.

Sample Problem 7

How many grams of chromic sulfide will be formed from 2.5 kg of chromic oxide according to the reaction?

$Cr_2O_3 + CS_2 \rightarrow Cr_2S_3 + CO_2$

Sample Problem 8

Butane weighing 120 grams is burned with 600 grams of O2:

$C_6H_{14} + O_2 \rightarrow H_2O + CO_2$

• If the reaction goes to 90% completion:

• Which is the Limiting and Excess reactant?

• What is the % Excess reactant?

• Illustrate the Law of Conservation of Mass.

Sample Problem 9

The Le Blanc Process for the manufacture of soda ash (Na2CO3) encompasses four steps:

1. $NaCl + H_2SO_4 \rightarrow NaHSO_4 + HCl$

2. $NaHSO_4 + NaCl \rightarrow Na_2SO_4 + HCl$

3. $Na_2SO_4 + C \rightarrow Na_2S + CO_2$

4. $Na_2S + CaCO_3 \rightarrow Na_2CO_3 + CaS$

• If only the first reaction was 75% complete, and all other reactants are supplied in excess, how many tonnes of soda ash are produced per 4 tonnes of salt?

• What is the minimum amount of C (in kg) required?

Sample Problem 10

Given the following reaction:

$HCl + KMnO_4 \rightarrow Cl_2 + MnCl_2 + KCl + H_2O$

• 3.7 L of an 86% by wt HCl solution with a specific gravity of 1.134 is made to react with 1.5 kg of KMnO4. Assuming the reaction is 88% complete:

• Which is the limiting and which is the excess reactant?

• Find the % excess reactant.

• Give the composition by weight of the materials after the reaction.

Additional info: These notes provide foundational concepts in chemical engineering calculations, including stoichiometry, process variables, concentration units, density, specific gravity, and limiting/excess reactant analysis. The sample problems illustrate practical applications of these concepts in industrial and laboratory settings.