Name: gas pressure in mixtures: partial pressures
Uploaded: 2020-09-03T13:38:26.000Z
Duration: 3 min 3 s
Channel: JoVE

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Mixtures of Gases: Dalton's Law of Partial Pressures and Mole Fractions

Ciśnienie czystego gazu to suma zderzeń molekularnych między jego cząstkami a otaczającymi powierzchniami. Próbka gazu zawierająca mniej cząstek w danej objętości wywiera niższe ciśnienie niż próbka zawierająca więcej cząstek w tej samej objętości. 

Ale jakie jest ciśnienie mieszaniny różnych gazów? W przypadku wieloskładnikowej mieszaniny gazów ciśnienie jest sumą zderzeń wszystkich cząsteczek gazu.

Zakłada się, że każdy składnik mieszaniny wywiera własne ciśnienie, które jest niezależne od innych obecnych gazów. Ciśnienie od dowolnego pojedynczego elementu nazywa się jego ciśnieniem cząstkowym. 

Całkowite ciśnienie mieszaniny gazów doskonałych jest równe sumie ciśnień cząstkowych jej składników. Ta obserwacja to prawo ciśnień cząstkowych Daltona.

Stosując prawo gazu doskonałego, ciśnienia cząstkowe poszczególnych składników gazu są podstawiane zmiennymi mierzalnymi.

Ponieważ gazy w mieszaninie zajmują tę samą objętość i mają tę samą temperaturę, równanie można uprościć.  

Suma moli poszczególnych składników jest równa całkowitej liczbie moli wszystkich składników gazu, nogółem. W związku z tym całkowite ciśnienie mieszaniny gazów jest równe ncałkowitemu pomnożonemu przez stałą RT w stosunku do V.

Liczba moli składnika podzielona przez całkowitą liczbę moli w mieszaninie to ułamek molowy.

Przegrupowanie ułamka molowego dla całkowitej liczby moli i podstawienie ncałkowitej liczby w prawie ciśnień cząstkowych Daltona daje wyrażenia dla ciśnienia całkowitego. Ponownie przestawiając, ciśnienie parcjalne gazu w mieszaninie jest iloczynem jego ułamka molowego i całkowitego ciśnienia mieszaniny.        

Tak więc w mieszaninie gazów ciśnienie parcjalne dowolnego składnika, i, jest równe ułamkowi molowemu i pomnożonemu przez ciśnienie całkowite.

Jako przykładowe obliczenia załóżmy, że pojemnik wypełniony dwoma gazami, helem i argonem, zawiera 40% objętości argonu. Oznacza to, że ułamek molowy argonu wynosi 0,4. Jeśli całkowite ciśnienie wynosi 4 atm, jakie jest ciśnienie parcjalne helu? 

Korzystając z równania ciśnienia cząstkowego gazu, ciśnienie parcjalne argonu jest równe jego ułamkowi molowemu pomnożonemu przez ciśnienie całkowite. Zatem 0,4 razy 4 atm daje ciśnienie parcjalne argonu jako 1,6 atm. 

Ponieważ suma ciśnień cząstkowych jest równa ciśnieniu całkowitemu, równanie można przeorganizować tak, aby ciśnienie parcjalne argonu można odjąć od ciśnienia całkowitego. Zatem ciśnienie parcjalne helu wynosi 2,4 atm.

mieszanki gazów: prawo daltona dotyczące ciśnień cząstkowych i ułamków molowych

Poszczególne gazy nie reagują ze sobą chemicznie, dlatego gazy w mieszaninie gazów nie wpływają na siebie nawzajem. Każdy gaz w mieszaninie wywiera takie samo ciśnienie, jakie wywierałby, gdyby znajdował się sam w pojemniku. Ciśnienie wywierane przez każdy pojedynczy gaz w mieszaninie nazywa się jego ciśnieniem cząstkowym.

Oznacza to, że w mieszaninie zawierającej trzy różne gazy A, B i C, jeśli PA jest ciśnieniem cząstkowym gazu A; PB to ciśnienie cząstkowe gazu B; PC to ciśnienie cząstkowe gazu C; wówczas całkowite ciśnienie jest określone równaniem 1:

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-01.png" style="height: 40px;">

Jest to prawo Daltona dotyczące ciśnień cząstkowych: całkowite ciśnienie mieszaniny gazów doskonałych jest równe sumie ciśnień cząstkowych gazów składowych.

Niech nA, nB i nC będą liczbą moli każdego z gazów w mieszaninie. Jeśli każdy gaz spełnia równanie gazu doskonałego, ciśnienie cząstkowe można zapisać jako:

<img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-02.png" style="height: 40px;">


Ponieważ wszystkie gazy mają tę samą temperaturę i zajmują tę samą objętość, podstawienie do równania 1 daje:

<img alt="Eq3" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-03.png" style="height: 40px;">


Równanie wskazuje, że w stałej temperaturze i stałej objętości całkowite ciśnienie próbki gazu jest określone przez całkowitą liczbę moli obecnego gazu.

W przypadku mieszanin gazów wygodnie jest wprowadzić wielkość zwaną ułamkiem molowym χ, który definiuje się jako liczbę moli danej substancji w mieszaninie podzieloną przez całkowitą liczbę moli wszystkich obecnych substancji. Matematycznie ułamek molowy substancji A w mieszaninie z B i C wyraża się jako

<img alt="Eq4" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-04.png" style="height: 40px;">


Podobnie ułamek molowy B i C wynosi;

<img alt="Eq5" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-05.png" style="height: 40px;">
<img alt="Eq6" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-06.png" style="height: 40px;">


Połączenie równania na ułamek molowy A i równania na ciśnienie cząstkowe daje:

<img alt="Eq7" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-07.png" style="height: 40px;">

Ciśnienie cząstkowe gazu A jest powiązane z ciśnieniem całkowitym mieszaniny gazów poprzez jej ułamek molowy.

Innymi słowy, ciśnienie gazu w mieszaninie gazów jest iloczynem jego ułamka molowego i całkowitego ciśnienia mieszaniny.

Mieszanki gazów: prawo Daltona dotyczące ciśnień cząstkowych i ułamków molowych

O ile poszczególne gazy nie reagują ze sobą chemicznie, poszczególne gazy w mieszaninie gazów nie wpływają wzajemnie na swoje ciśnienie. Każdy gaz ...

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gas pressure in mixtures: partial pressures

Gas pressure in mixtures is described by partial pressure and mole fraction. When gases do not chemically react, each gas in the mixture acts as if it were alone in the container. The pressure from one gas is called its partial pressure.

For a mixture of three gases, A, B, and C, the total pressure equals the sum of their partial pressures: PA, PB, and PC. This is Dalton's law of partial pressures. It states that the total pressure of a mixture of ideal gases is the sum of the pressures from each gas.

If each gas follows the ideal-gas equation, its partial pressure can be written in terms of moles, temperature, and volume. Because every gas in the mixture has the same temperature and takes up the same volume, these terms can be combined. At constant temperature and constant volume, the total pressure depends on the total number of moles of gas present.

For gas mixtures, chemists also use mole fraction, x. Mole fraction is the number of moles of one substance divided by the total number of moles in the mixture. For gas A in a mixture with B and C, the mole fractions of A, B, and C are found in this way.

Mole fraction also links directly to partial pressure. The partial pressure of gas A equals its mole fraction times the total pressure of the mixture. In other words, a gas's pressure in a mixture is its share of the total pressure.

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Gas Pressure in Mixtures: Partial Pressures

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