Question

If 2.0 mol of gas A is mixed with 1.0 mol of gas B to give a total pressure of 1.6 atm, what is the partial pressure of gas A and B?

A) PA = 0.33 atm and PB = 0.67 atm

B) PA = 0.67 atm and PB = 0.33 atm

C) PA = 1.0 atm and PB = 2.0 atm

D) PA = 2.0 atm and PB = 1.0 atm

E) PA = 1.06 atm and PB = 0.53 atm

Answer 1

Dalton’s Law states that the partial pressure of an ideal gas is equal to the total pressure of the system.

Knowing that 3 moles total of gas in the tank. The partial pressure of A must be 2/3 of the total and partial pressure B must be 1/3 of total so the answer is E.

Answer 2

The partial pressure of gas A and B is option E) PA = 1.06 atm and PB = 0.53 atm

Step-by-step explanation:

The pressure exerted by a particular gas in a mixture is known as its partial pressure. Then, Dalton's law states that the total pressure of a gas mixture is equal to the sum of the pressures that each gas would exert if it were alone:

PT = PA + PB

Dalton's partial pressure law can also be expressed in terms of the molar fraction of the gas in the mixture. The molar fraction is a dimensionless quantity that expresses the relationship of the number of moles of a component with the number of moles of all the components present.

The molar fraction of a gas A in a gas mixture is given by:

`XA=(nA)/(nT)`

where nA is the amount of moles of gas A and nT is the amount of total moles.

This fraction will always be less than 1.

Then in a mixture of two or more gases, the partial pressure of the gas A can be expressed as:

PA = XA * PT

In this case you know that the total pressure PT is 1.6 atm.

You also know that 2.0 mol of gas A is mixed with 1.0 mol of gas B. Then the total number of moles will be 3 (2 moles of A plus 1 mole of B). Then you can calculate the mole fraction of gas A and gas B as:

`XA=(2 moles)/(3 moles) =(2)/(3)`

`XB=(1 moles)/(3 moles) =(1)/(3)`

Then, the partial pressure of the gas A and the partial pressure of the gas B can be expressed as:

`PA=(2)/(3) *1.6 atm=1.06 atm`

`PB=(1)/(3) *1.6 atm=0.53 atm`

Finally, the partial pressure of gas A and B is option E) PA = 1.06 atm and PB = 0.53 atm