A sample of PCl5 weighing 2.69 grams is placed in a 1.000 liter flask and vaporized completely at 250 o C.
The final pressure observed at this temperature is 1.000 atmospheres. Note that some, but not all of the PCl5 decomposes according to the equation: PCl5 (g) ---------> PCl3 (g) + Cl2 (g)
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To solve this question, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
We have the following information:
- The pressure (P) is given as 1.000 atmospheres.
- The volume (V) is given as 1.000 liters.
- The temperature (T) is given as 250°C. However, we need to convert this to Kelvin by adding 273 to the Celsius temperature: T = 250 + 273 = 523 K.
Now, we need to determine the number of moles (n) of PCl5 in the sample. To do this, we'll use the molar mass of PCl5, which is:
Molar Mass of PCl5 = (1*Molar Mass of P) + (5*Molar Mass of Cl)
The molar masses are:
Molar Mass of P = 31.0 g/mol
Molar Mass of Cl = 35.5 g/mol
Now, let's calculate the molar mass of PCl5:
Molar Mass of PCl5 = (1*31.0 g/mol) + (5*35.5 g/mol) = 207.5 g/mol
Next, we can calculate the number of moles of PCl5 using its given mass:
Number of moles of PCl5 = Mass of PCl5 / Molar Mass of PCl5
Number of moles of PCl5 = 2.69 g / 207.5 g/mol
Now, we can substitute the values into the ideal gas law equation to find the final volume of the gases produced (PCl3 and Cl2) after the decomposition.
(1.000 atm)(1.000 L) = nRT
(1.000 atm)(1.000 L) = (Number of moles of PCl3 + Number of moles of Cl2)(0.0821 L.atm/mol.K)(523 K)
We have the number of moles of PCl5, and we know from the balanced chemical equation that each mole of PCl5 produces one mole of PCl3 and one mole of Cl2.
Thus, we can calculate:
Number of moles of PCl3 = Number of moles of PCl5
Number of moles of Cl2 = Number of moles of PCl5
Finally, we can substitute these values into the equation to find the final volume of the gases.