A 30.9 L cylinder containing C2H4F2 at a pressure of 114.0 torr is connected by a valve to 0.865 L cylinder containing C4H10 at 114.0 torr pressure. Calculate the partial pressure (atm) of C4H10 when the valve is opened.
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To calculate the partial pressure of C4H10 when the valve is opened, we need to use the ideal gas law equation, which is:
PV = nRT
where:
P = pressure (in atm)
V = volume (in liters)
n = moles of gas
R = gas constant (0.0821 L · atm / (mol · K))
T = temperature (in Kelvin)
First, let's calculate the number of moles of C2H4F2 using the given information. We know that the pressure and volume of the cylinder containing C2H4F2 are 114.0 torr (which is equivalent to 0.150 atm) and 30.9 L, respectively.
n(C2H4F2) = PV / RT
n(C2H4F2) = (0.150 atm) * (30.9 L) / (0.0821 L·atm/(mol·K))
Next, let's calculate the number of moles of C4H10. We know the pressure and volume of the cylinder containing C4H10 are 114.0 torr (equivalent to 0.150 atm) and 0.865 L, respectively.
n(C4H10) = PV / RT
n(C4H10) = (0.150 atm) * (0.865 L) / (0.0821 L·atm/(mol·K))
Now, since the reaction is happening at constant temperature and volume, the moles of gas will remain the same before and after the valve is opened. So the number of moles of C4H10 will be equal to the moles of C2H4F2.
n(C4H10) = n(C2H4F2)
Finally, we can use the number of moles of C4H10 and the total volume to calculate the partial pressure of C4H10.
P(C4H10) = n(C4H10) * RT / V(total)
P(C4H10) = (n(C2H4F2) * (0.0821 L·atm/(mol·K))) / (30.9 L + 0.865 L)
Solving this equation will give you the partial pressure of C4H10 when the valve is opened.