User:Pierantonio Gratarol



The Gratarolo family is originally from Bergamo; but in Venice there were several of them with this surname, I don't know if more than one of them had hired this family, or if it was the family itself. Others practise marketing, possessing their own ships and capital for worth 50 thousand ducats, another 1' lawyer, and medicine; other employees were the ducal secretary. In the chronicles there is an excellent orator Andrea oratore, father of Giambattista prior to the hospitable house of God, a Venturino, and a secretary Jerome living all at the beginning of the seventeenth century. In recent years Pierantonio became among us Pierantonio's son of Giuseppe, whose brief article I have been allowed here. Pierantonio was about fourteen years old when his father died, and he was in 1752. After having been under the discipline of the famous Doctor Natale dalle Laste. began in the Ducal cancellaria. In 1772 he was promoted to Secretary of the Senate, and where he left with the ambasctator Pietro Contarini who was the attorney of a. Marco, to welcome the inhalation of Vittorio Amadeo III at the throne. King of Sardinia, but the embassy was suppressed. Elected in 1773 and resident in Turin, his departure also here did not take place, because in the following year the Republic suspended to send to the Court his ministers. In the meantime Gratarol could turn a part of Lombardy, and Tuscany, and visit Rome, and Naples, where I then returned to the figure of resident names' born in 1776, if he could get the commissions of money necessary for the departure. I am a man as talented as I am of talent and vivacity of spirit provided, as light and devoted to love, he committed some, very well known here, young imprudence, totally disgraceful to the gravity and jealousy of ministry, to which he covered. He is therefore the subject of public rumours, even ridiculously placed on public scenes. and what is most important, in the misfortune of the government, knew that his homeland was no longer a quiet asylum for him _ And in effect in September 1777, however forbidden it was for the secretaries to move away from' Venetian borders without superior permission, parts unexpectedly directing his trip to Brunswich where from that Court was very well received. It passed then to Stockolm, and arrived there after mid-March 1778. In the meantime, he was brought to a rigorous trial in Venice and was called to carve himself into prison. He was sentenced to death and seized his property, which had been forfeited by the states of the republic on 22 December 1777. From Stockholm in 1780 he went to England, and here from the knight and member of the parliament Morton Pitt was filled with favours; he gave him accommodation in his country, lent them in several instalments the sum of eight thousand sticks, part of which the Gratorol paid for various debts, and part reserved for some great project, hoping to establish himself in London in any public sector; and He passed posture in America. and in 1784 he was in Baltimore, a town in the province of Maryland. At the 25th of October that year, Baltimore left Baltimore with other wayfarers and travelled to Brazil, where he took land in gennaro l785. Beyond fe' vela to 7 March and arrived in July to the island of Madagascar. The captain of the vessel that had seized other vessels, abandoned the wayfarers, stealing them, and the Gratarol lost its effects which amounted to more than 800 pounds sterling. Finally in early October of the same year 1785 surmounted by a disease that destroyed most of the company, not without suspicion of being eglino were poisoned by the people of the country, Moors at 8, or 9 leagues distant from the place of landing.

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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