A mixture of He, N2, and Ar has a pressure of 14.2 atm at 28.0 °C. If the partial pressure of He is 1525 torr and that of Ar is 2807 mm Hg, what is the partial pressure of N2?
Ptotal = pHe + pN2 + pAr
You know all but one unknown.
Be careful with the units. Ptotal is in atm and the gases are given in torr (and mm but 1 mm = 1 torr)
To find the partial pressure of N2 in the mixture, we need to use Dalton's law of partial pressures, which states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the individual gases.
First, let's convert the given pressure values to a consistent unit. We can choose to convert everything to atmospheres (atm) for convenience.
Given:
Partial pressure of He = 1525 torr
Partial pressure of Ar = 2807 mmHg
Total pressure = 14.2 atm
To convert torr to atm, divide by 760:
Partial pressure of He = 1525 torr ÷ 760 torr/atm = 2.01 atm
To convert mmHg to atm, divide by 760:
Partial pressure of Ar = 2807 mmHg ÷ 760 mmHg/atm = 3.69 atm
Now, let's use Dalton's law to find the partial pressure of N2.
Total pressure = Partial pressure of He + Partial pressure of N2 + Partial pressure of Ar
14.2 atm = 2.01 atm + Partial pressure of N2 + 3.69 atm
To solve for the partial pressure of N2, rearrange the equation:
Partial pressure of N2 = Total pressure - Partial pressure of He - Partial pressure of Ar
Partial pressure of N2 = 14.2 atm - 2.01 atm - 3.69 atm
Partial pressure of N2 = 8.5 atm
Therefore, the partial pressure of N2 in the mixture is 8.5 atm.
To find the partial pressure of N2, we need to subtract the partial pressures of He and Ar from the total pressure of the mixture.
Step 1: Convert the partial pressures of He and Ar to atm.
To convert from torr to atm, divide the pressure by 760:
Partial pressure of He = 1525 torr / 760 torr/atm = 2.00658 atm
Partial pressure of Ar = 2807 mm Hg / 760 mm Hg/atm = 3.69145 atm
Step 2: Find the partial pressure of N2.
Total pressure of the mixture = Pressure of He + Pressure of N2 + Pressure of Ar
14.2 atm = 2.00658 atm + Pressure of N2 + 3.69145 atm
Step 3: Solve for the partial pressure of N2.
Pressure of N2 = 14.2 atm - 2.00658 atm - 3.69145 atm
Pressure of N2 = 8.50297 atm
Therefore, the partial pressure of N2 is approximately 8.5 atm.