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# मोल अंश

(अणु-अंश से अनुप्रेषित)

रसायन विज्ञान में, किसी मिश्रण के किसी अवयव का मोल अंश या मोल प्रभाजकहते है (mole fraction या molar fraction ; संकेत : ${\displaystyle x_{i}}$) निम्नलिखित प्रकार से पारिभाषित है-

${\displaystyle x_{i}={\frac {n_{i}}{n_{tot}}}}$

जहाँ,

${\displaystyle n_{i}}$ = अवयव के मोलों की संख्या

तथा,

${\displaystyle \sum _{i=1}^{N}n_{i}=n_{tot};\ ;\sum _{i=1}^{N}x_{i}=1}$

अर्थात सभी अवयवों के अणु-अंशों का योग 1 होता है।

## अणु-अंश के गुण

अणु-अंश का उपयोग प्रायः प्रावस्था आरेख (phase diagram) के निर्माण में किया जाता है। इसके अनेक लाभ हैं-

• यह ताप पर निर्भर नहीं है। (such as molar concentration) and does not require knowledge of the densities of the phase(s) involved
• a mixture of known mole fraction can be prepared by weighing off the appropriate masses of the constituents
• the measure is symmetric: in the mole fractions x=0.1 and x=0.9, the roles of 'solvent' and 'solute' are reversed.
• In a mixture of ideal gases, the mole fraction can be expressed as the ratio of partial pressure to total pressure of the mixture

## मोल अंश से सम्बन्धित अन्य राशियाँ

### Mass fraction

The mass fraction ${\displaystyle w_{i}}$ can be calculated using the formula

${\displaystyle w_{i}=x_{i}\cdot {\frac {M_{i}}{M}}}$

where ${\displaystyle M_{i}}$ is the molar mass of the component ${\displaystyle i}$ and ${\displaystyle M}$ is the average molar mass of the mixture.

Replacing the expression of the molar mass:

${\displaystyle w_{i}=x_{i}\cdot {\frac {M_{i}}{\sum _{i}x_{i}M_{i}}}}$

### अणु प्रतिशत (Mole percentage)

Multiplying mole fraction by 100 gives the mole percentage, also referred as amount/amount percent (abbreviated as n/n%).

### Mass concentration

The conversion to and from mass concentration ${\displaystyle \rho _{i}}$ is given by:

${\displaystyle x_{i}={\frac {\rho _{i}}{\rho }}\cdot {\frac {M}{M_{i}}}}$

where ${\displaystyle M}$ is the average molar mass of the mixture.

${\displaystyle \rho _{i}=x_{i}\rho \cdot {\frac {M_{i}}{M}}}$

### Molar concentration

The conversion to molar concentration ${\displaystyle c_{i}}$ is given by:

${\displaystyle c_{i}={\frac {x_{i}\cdot \rho }{M}}=x_{i}c}$

or

${\displaystyle c_{i}={\frac {x_{i}\cdot \rho }{\sum _{i}x_{i}M_{i}}}}$

where ${\displaystyle M}$ is the average molar mass of the solution, c total molar concentration and ${\displaystyle \rho }$ is the density of the solution .

### Mass and molar mass

The mole fraction can be calculated from the masses ${\displaystyle m_{i}}$ and molar masses ${\displaystyle M_{i}}$ of the components:

${\displaystyle x_{i}={\frac {\frac {m_{i}}{M_{i}}}{\sum _{i}{\frac {m_{i}}{M_{i}}}}}}$