2. Alex, a fresh graduate chemical engineer, started his job by a mission requested by his boss. He was supposed to prepare a small amount of ethylene in the lab, to use it later for polyethylene synthesis. His boss, OE, also known as “The Monster” did not provide him any information on how to prepare the ethylene. Alex then looked in Wikipedia and found that ethylene can be prepared in the lab by the dehydration of ethyl alcohol, according to the equation
C2H5OH C2H4 + H2O
Alex started his experiment with 250 ml ethyl alcohol, on a day when lab temperature was 27oC and pressure was 754 mm Hg. “The Monster” told Alex to keep all the produced ethylene in a small cylinder whose volume is 5 L. What is the pressure inside this cylinder?
For trial and error use one trial only
i don't know the answer. please give the calculation
To determine the pressure inside the cylinder, we need to use the ideal gas law equation, which is:
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)
To start, we need to convert the given temperature from degrees Celsius to Kelvin. The conversion formula is:
T(K) = T(°C) + 273.15
So, in this case, the temperature in Kelvin would be:
T = 27°C + 273.15 = 300.15 K
Next, we need to calculate the number of moles of ethylene produced. We can use stoichiometry to relate the number of moles of ethylene to the number of moles of ethyl alcohol. The balanced chemical equation tells us that 1 mole of C2H5OH will produce 1 mole of C2H4.
Given that Alex started with 250 ml of ethyl alcohol, we can convert this volume to moles using the molar volume of a gas at standard temperature and pressure (STP), which is 22.4 liters per mole. The conversion is:
n(C2H5OH) = V(C2H5OH) / V(molar volume at STP)
n(C2H5OH) = 250 ml / (22.4 L/mol)
n(C2H5OH) = 0.01116 mol
Therefore, 0.01116 moles of C2H4 are produced.
Now, we can substitute the values into the ideal gas law equation:
PV = nRT
P(5 L) = (0.01116 mol)(0.0821 L·atm/mol·K)(300.15 K)
P(5 L) = 0.13618 atm
Finally, we divide the pressure by the volume of the cylinder to find the pressure inside the cylinder:
Pressure inside the cylinder = 0.13618 atm / 5 L
Pressure inside the cylinder ≈ 0.02724 atm
Therefore, the pressure inside the cylinder is approximately 0.02724 atm or 20.55 mm Hg.