a mixture of N2, O2 and Ar have mole fractions of 0.25, 0.65, and 0.10, respectively. What is the pressure of N2 if the total pressure of the mixture is 3.9 atm?
pN2 = XN2*Ptotal
0.963
To find the pressure of N2 in the mixture, we need to use the mole fraction and the total pressure of the mixture.
Step 1: Convert the mole fractions to decimal form.
- The mole fraction of N2 is 0.25.
- The mole fraction of O2 is 0.65.
- The mole fraction of Ar is 0.10.
Step 2: Calculate the partial pressure of N2.
- The partial pressure of N2 is equal to the mole fraction of N2 multiplied by the total pressure of the mixture.
- Partial pressure of N2 = Mole fraction of N2 x Total pressure of the mixture
- Partial pressure of N2 = 0.25 x 3.9 atm
Step 3: Calculate the partial pressure of N2.
- Partial pressure of N2 = 0.975 atm
The pressure of N2 in the mixture is 0.975 atm.
To calculate the partial pressure of N2 in the mixture, we can use Dalton's Law of partial pressures. According to this law, the total pressure of a mixture of gases is equal to the sum of the partial pressures of each gas in the mixture.
In this case, we know the mole fractions of N2, O2, and Ar. A mole fraction indicates the fraction of the total number of moles contributed by a particular gas component. In other words, the mole fraction of N2 is 0.25, which means that for every 1 mole total of all gases, there are 0.25 moles of N2.
We can calculate the moles of N2 as follows:
moles of N2 = mole fraction of N2 * total moles of all gases
= 0.25 * total moles of all gases
Similarly, moles of O2 and Ar can be calculated using their respective mole fractions:
moles of O2 = mole fraction of O2 * total moles of all gases
= 0.65 * total moles of all gases
moles of Ar = mole fraction of Ar * total moles of all gases
= 0.10 * total moles of all gases
Now, let's substitute these values into Dalton's Law:
total pressure = partial pressure of N2 + partial pressure of O2 + partial pressure of Ar
Solving for the partial pressure of N2, we get:
partial pressure of N2 = total pressure - (partial pressure of O2 + partial pressure of Ar)
substituting the values we have:
partial pressure of N2= 3.9 atm - (0.65 * 3.9 atm + 0.10 * 3.9 atm)
partial pressure of N2 = 3.9 atm - (2.535 atm + 0.39 atm)
partial pressure of N2 = 3.9 atm - 2.925 atm
partial pressure of N2 = 0.975 atm
Therefore, the partial pressure of N2 in the mixture is 0.975 atm.