# Constants and Conversions

$$Joules$$ = $$Coulombs$$$$\cdot$$$$Volts$$ = $$Kilograms$$$$\cdot$$$$\frac{meters^{2}}{seconds^2}$$

$$Power$$ = $$Current$$$$\cdot$$$$Volts$$  in units $$\frac {Joules}{seconds}$$

Keep in mind that there are two systems for using units - the MKS and cgs system. The MKS system uses meters, kilograms, and seconds together. The cgs system uses centimeters, grams, and seconds together

Also keep in mind that there are multiple meanings for $$R$$. $$R$$, like $$V$$, is a commonly used letter for formulas in the physical sciences. It is imperative to keep track of what $$R$$ you are talking about. For physical chemistry specifically, $$R$$ can mean four different things.

1. Rydberg constant, R. Seen in $$E=-R\frac{1}{n^2}$$
2. Radial function, R. Seen in $$\psi = R_{n\ell}Y_{\ell}^{m}$$
3. Bond length R. Seen in the moment of inertia formula for a rigid rotor $$I=\mu\ R^2$$
4. Constant R. Seen in the ideal gas law $$PV=nRT$$

Below are the conversions between energy units:

 $$joule$$ $$\frac {kJ}{mol}$$ $$eV$$ $$E_h$$ $$cm^{-1}$$ $$Hz$$ $$1 joule$$ $$1$$ $$6.022x10^{20}$$ $$6.241x10^{18}$$ $$2.294x10^{17}$$ $$5.034x10^{22}$$ $$1.509x10^{33}$$ $$1 \frac {kJ}{mol}$$ $$1.660x10^{-21}$$ $$1$$ $$1.036x10^{-2}$$ $$3.809x10^{-4}$$ $$83.596$$ $$2.506x10^{12}$$ $$1 eV$$ $$1.602x10^{-19}$$ $$96.485$$ $$1$$ $$3.675x10^{-2}$$ $$8065.54$$ $$2.418x10^{14}$$ $$1 E_h$$ $$4.359x10^{-18}$$ $$2625.500$$ $$27.211$$ $$1$$ $$2.1947x10^{5}$$ $$6.580x10^{15}$$ $$1 cm^{-1}$$ $$1.986x10^{-23}$$ $$1.196x10^{-2}$$ $$1.239x10^{-4}$$ $$4.556x10^{-6}$$ $$1$$ $$2.998x10^{10}$$ $$1 Hz$$ $$6.626x10^{-34}$$ $$3.990x10^{-13}$$ $$4.135x10^{-15}$$ $$1.159x10^{-16}$$ $$3.336x10^{-11}$$ $$1$$

Below are the values of various physical constants

 Constant Symbol Value Atomic mass constant $$m_u$$ $$1.6605402x10^{-27} kg$$ Avogadro constant $$N_A$$ $$6.0221367x10^{23} mol^{-1}$$ Bohr magneton $$\beta_B$$ = $$\frac {e\hbar}{2m_e}$$ $$9.2740154x10^{-24} J \cdot\ T^{-1}$$ Bohr radius $$a_0$$ = $$\frac {4\pi\epsilon_0}{m_e e^{2}}$$ $$5.29177249x10^{-11} m$$ Boltzmann constant $$k_B$$ $$1.380658x10^{-23} J \cdot\ K^{-1}$$ $$.695038 cm^{-1}$$ Electron rest mass $$m_e$$ $$9.1093897x10^{-31} kg$$ Gravitational constant $$G$$ $$6.67259x10^-11 m^3 \cdot\ kg^{-1} \cdot\ s^{-2}$$ Molar gas constant $$R$$ $$8.314510 J \cdot\ K^{-1} \cdot\ mol^{-1}$$ $$.0831451 dm^3 \cdot\ bar \cdot\ K^{-1} \cdot\ mol^{-1}$$ $$.0820578 dm^3 \cdot\ atm \cdot\ K^{-1} \cdot\ mol^{-1}$$ Molar volume, ideal gas one bar, 0$$^\circ$$C $$22.71108 L \cdot\ mol^{-1}$$ one atm, 0$$^\circ$$C $$22.41409 L \cdot\ mol^{-1}$$ Nuclear magneton $$\mu_n$$ = $$\frac {e\hbar}{2m_p}$$ $$5.0507866x10^{-27} J \cdot\ T^{-1}$$ Permittivity of vacuum $$\epsilon_0$$ $$8.854187816x10^{-12} C^2 \cdot\ J^{-1} \cdot\ m^{-1}$$ $$4\pi\epsilon_0$$ $$1.112650056x10^{-10} C^2 \cdot\ J^{-1} \cdot\ m^{-1}$$ Planck constant $$h$$ $$6.6260755x10^{-34} J \cdot\ s$$ $$\hbar$$ $$1.05457266x10^{-34} J \cdot\ s$$ Proton charge $$e$$ $$1.60217733x10^{-19} C$$ Proton magnetogyric ratio $$\gamma_p$$ $$2.67522128x10^8 s^{-1} \cdot\ T^{-1}$$ Proton rest mass $$m_p$$ $$1.6726231x10^{-27} kg$$ Rydberg constant (Bohr) $$R_\infty$$ = $$\frac {m_e e^4}{8\epsilon^2 _0 h^2}$$ $$2.1798736x10^{-18} J$$ $$109737.31534 cm^{-1}$$ Rydberg constant (experimental) $$R_h$$ $$109677.581 cm^{-1}$$ Speed of light in vacuum $$c$$ $$299792458 m \cdot\ s^{-1}$$