User:MagnInd

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Constantin Budeanu was a Romanian electrical engineer born in 1886.In 1903-1908 the National School of Bridges and Highways in Bucharest, Romanian Railways and the Bucharest Tram Society technical director of the Electrical Society in Bucharest.
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In 1916 became professor of Electrical Measurements and Electrical Engineering in the Electricity and Electrical Engineering department of the National School of Bridges and Highways, being assistant to Nicolae Vasilescu Karpen.

Molar mass

 * $$ \bar{M} = \sum_i x_i M_i \,$$

It can also be calculated from the mass fractions $$w_i$$ of the components:


 * $$ 1/\bar{M} = \sum_i \frac ,$$


 * $$ x_i= \frac ,$$

Relation to mass concentration
The relation between mass concentration $$\rho_i$$ and molar concentration is:


 * $$\boldsymbol{\rho_i} = c_i \cdot M_i$$

where $$M_i$$ is the molar mass of constituent $$i$$.

Relation to mass fraction

 * $$\rho \cdot w_i = c_i \cdot M_i$$


 * $$w_i = \frac{1}{1+1/(m_i\cdot M_i)}$$


 * $$c_i = \rho \cdot \frac{m_i}{1+ m_i\cdot M_i}$$


 * $$ m_i = \frac \,$$

Relation to molality

 * $$ \frac = m_i \,$$ or

The sum of the molar concentrations of all components (including the solvent) gives the multiplicative inverse of the molar volume of the mixture or the molar density $$\rho$$ of the solution:


 * $$ \frac = \sum_i c_i \,$$

Thus, for pure component the molar concentration equals the molar density of the mixture namely density divided by average molar mass of the mixture M.

Relation to mole fraction
Molar concentration is the product of the density of a solution and the mole fraction $$w_i$$ of a component:


 * $$\frac = \frac \cdot x_i$$

Volume dependence
In order to avoid confusion and also to underline the significance (the connection between the two quantities mass concentration and mass density), the best solution is to use bolded rho or $$\varrho_i \,$$ for mass concentration while keeping the unmodified rho for mass density. This implies that any other Wikipedia requirements which might be contrary to this purpose be ignored.
 * Volume fraction
 * Volume percent
 * Volume concentration
 * Molality


 * $$\rho = \sum_i \varrho_i \,$$



V \approx V_0 (1 + \alpha \cdot \Delta T)

$$
 * $$\rho = \frac $$

Expressed as a function of the densities of pure components of the mixture and their volume participation, it reads:


 * $$\rho = \sum_i \rho_i^{*,0} \frac{V_i}{V}\,= \rho_i^* \frac{n_i V_i^*}{V}\,$$
 * $$\rho_i = \varrho_i \frac{V_i}{V}\,= \rho_i^* \frac{n_i V_i^*}{V}\,$$
 * $$\alpha_i = \sum_i x_i \cdot \frac \cdot \bar{\alpha_i}$$
 * $$\alpha_i = \sum_i c_i \cdot \bar \cdot \bar{\alpha_i}$$
 * $$1 = \sum_i c_i \cdot \bar{V_i}$$

$$\phi_i = \frac = \frac$$

Gradient

 * Fick's laws of diffusion
 * Concentration gradient
 * Transport phenomena
 * Mass transfer
 * Maxwell-Stefan diffusion

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