Utilities

A collection of useful constants and functions used in chemical engineering. Below is a list of available sections.

  1. Fundamental constants
  2. Error functions
  3. Trigonometric functions
  4. Inverse trigonometric functions
  5. Hyperbolic functions
  6. Bessel functions

Fundamental constants

Physical constants used in chemical engineering.

Atomic mass unit, \(Da\) or \(u\) 1.66053906660(50)×10-27 kg
Avogadro's number, \(N_\text{A}\) 6.022142×1023 mol⁻¹
Boltzmann's constant, \(k_\text{B}\) 1.380649×10-23 J K⁻¹
8.617333262145×10-5 eV K⁻¹
Electron charge, \(q_\text{e}\) 1.602176634×10-19 C
Electron mass, \(m_\text{e}\) 9.1093837015(28)×10-31 kg
Faraday's constant, \(F\) 96485.33212 C mol⁻¹
Gas constant, \(R\) 8.31446261815324 J K⁻¹ mol⁻¹
0.0831446261815324 L bar K⁻¹ mol⁻¹
0.082057366080960 L atm K⁻¹ mol⁻¹
1.98720425864083×10-3 kcal K⁻¹ mol⁻¹
8.20573660809596×10-5 m³ atm K⁻¹ mol⁻¹
8314.46261815324 L Pa K⁻¹ mol⁻¹
Gravitational acceleration, \(g\) 9.80665 m s²
Molar volume (STP), \(V_\text{m}\) 0.024789570296023 m³ mol⁻¹
Neutron mass, \(m_\text{n}\) 1.67492749804(95)×10-27 kg
Proton mass, \(m_\text{p}\) 1.67262192369(51)×10-27 kg
Planck's constant, \(h\) 6.62607015×10-34 J Hz⁻¹
Speed of light, \(c\) 2.99792458×108 m s⁻¹

Error functions

Calculate the error function, \(\text{erf}(x)\), and complementary error function, \(\text{erfc}(x)\), values for a given \(x\).

\(x\)
\(\text{erf}(x)\)
\(\text{erfc}(x)\)

Trigonometric functions

Calculate the value of several trigonometric functions for a given \(\theta\).

\(\theta\)
The input accepts pi as \(\pi\). For instance, you can enter pi/2.
\(\text{sin}(\theta)\)
\(\text{cos}(\theta)\)
\(\text{tan}(\theta)\)
\(\text{cotan}(\theta)\)
\(\text{sec}(\theta)\)
\(\text{cosec}(\theta)\)

Inverse trigonometric functions

Calculate the value of several inverse trigonometric functions for a given \(x\).

\(x\)
\(\text{arcsin}(x)\)
\(\text{arccos}(x)\)
\(\text{arctan}(x)\)
\(\text{arccot}(x)\)
\(\text{arcsec}(x)\)
\(\text{arccsc}(x)\)

Hyperbolic functions

Calculate the value of several hyperbolic functions for a given \(x\).

\(x\)
\(\text{sinh}(x)\)
\(\text{cosh}(x)\)
\(\text{tanh}(x)\)
\(\text{cotanh}(x)\)
\(\text{sech}(x)\)
\(\text{cosech}(x)\)

Bessel functions

Calculate the value of several Bessel functions for a given \(x\).

Value
Order