Utilities

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

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