A 250 ml cylinder containing C2H4 at a pressure of 1.00 atm is connected by a valve to 950 ml cylinder containing PF3 at 2.50 atm pressure. Calculate the partial pressure (atm) of Pf3 when the valve is opened.
(2.5 atm)(.950 L)=x(1.2L)
=2.0 atm
To calculate the partial pressure of PF3 when the valve is opened, we first need to understand the concept of partial pressure. Partial pressure is the pressure exerted by an individual gas component in a mixture of gases. It is proportional to the mole fraction of that particular gas component.
To find the partial pressure of PF3, we can use Dalton's Law of Partial Pressures, which states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases.
Using Dalton's Law, we can calculate the partial pressure of C2H4 and PF3 separately.
Given:
- Volume of the C2H4 cylinder = 250 ml = 0.250 L
- Pressure of C2H4 cylinder = 1.00 atm
- Volume of the PF3 cylinder = 950 ml = 0.950 L
- Pressure of PF3 cylinder = 2.50 atm
Step 1: Convert the volumes to liters for both gases.
- Volume of C2H4 = 0.250 L
- Volume of PF3 = 0.950 L
Step 2: Calculate the partial pressure of C2H4 using the ideal gas law.
- PV = nRT (where P is pressure, V is volume, n is moles, R is the ideal gas constant, and T is temperature)
- Rearrange the formula to solve for moles: n = PV / RT
- Calculate the number of moles of C2H4 using the given pressure, volume, and temperature (we assume constant):
- n(C2H4) = (1.00 atm) * (0.250 L) / (0.0821 L·atm/mol·K * T)
- We don't have the temperature, so we can assume it is constant and cancel it out.
- n(C2H4) = (1.00 atm) * (0.250 L) / (0.0821 L·atm/mol·K)
- n(C2H4) ≈ 0.01214 mol
Step 3: Calculate the partial pressure of PF3 using Dalton's Law of Partial Pressures.
- We know that the total pressure (PTotal) = P(C2H4) + P(PF3)
- Rearrange the formula to solve for P(PF3): P(PF3) = PTotal - P(C2H4)
- Substitute the values: P(PF3) = (2.50 atm) - (1.00 atm)
- P(PF3) = 1.50 atm
Therefore, the partial pressure of PF3 when the valve is opened is 1.50 atm.