C2H6 <> C2H4 + H2. when 1.00mol ethane is cracked at 180kPa and 1000K, the yield of ethene is 0.36mol. Calculate the value Kp at 1000K...
To calculate the value of Kp at 1000K, we can use the equation:
Kp = (P(C2H4) * P(H2)) / P(C2H6)
where P(C2H4), P(H2), and P(C2H6) are the partial pressures of ethene, hydrogen, and ethane, respectively.
Given that 1.00 mol of ethane (C2H6) is cracked and the yield of ethene (C2H4) is 0.36 mol, we can determine the number of moles of ethane remaining:
Moles of ethane remaining = 1.00 mol - 0.36 mol = 0.64 mol
Since the reaction takes place at 180 kPa, we can assume that the total pressure is 180 kPa.
Now, we need to convert the moles to partial pressures using the ideal gas law:
PV = nRT
where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant (0.0821 L∙atm/(mol∙K)), and T is temperature in Kelvin.
For ethene (C2H4):
P(C2H4) = (moles of C2H4 * R * T) / V
P(C2H4) = (0.36 mol * 0.0821 L∙atm/(mol∙K) * 1000 K) / V
P(C2H4) = 29.736 L∙atm / V
Similarly, for hydrogen (H2):
P(H2) = (moles of H2 * R * T) / V
P(H2) = (0.36 mol * 0.0821 L∙atm/(mol∙K) * 1000 K) / V
P(H2) = 29.736 L∙atm / V
Finally, for ethane (C2H6):
P(C2H6) = (moles of C2H6 * R * T) / V
P(C2H6) = (0.64 mol * 0.0821 L∙atm/(mol∙K) * 1000 K) / V
P(C2H6) = 52.864 L∙atm / V
Substituting these values into the equation for Kp:
Kp = (P(C2H4) * P(H2)) / P(C2H6)
Kp = (29.736 L∙atm / V) * (29.736 L∙atm / V) / (52.864 L∙atm / V)
Kp = (29.736 * 29.736) / 52.864
Kp = 16.738
Therefore, the value of Kp at 1000K is approximately 16.738.
To calculate the value of Kp at 1000K, we need to use the given information about the reaction and the stoichiometry of the equation.
First, let's write the balanced equation for the reaction:
C2H6 ⇌ C2H4 + H2
The coefficients in this equation represent the molar ratios of the reactants and products. From the equation, we can see that 1 mol of ethane (C2H6) yields 1 mol of ethene (C2H4) and 1 mol of hydrogen gas (H2).
Given:
- Initial moles of ethane (C2H6): 1.00 mol
- Moles of ethene (C2H4) produced: 0.36 mol
To calculate the value of Kp, we need to use the following formula:
Kp = (P(C2H4) * P(H2)) / (P(C2H6))
Where:
P(C2H4) = partial pressure of ethene
P(H2) = partial pressure of hydrogen gas
P(C2H6) = partial pressure of ethane
We need to find the partial pressures of the gases. Since the reaction takes place at 180kPa, we can assume that the total pressure is 180kPa.
To find the partial pressure of ethene (C2H4), we use the moles of ethene and divide it by the total moles of gases present:
P(C2H4) = (moles of ethene) / (total moles of gases)
P(C2H4) = 0.36 mol / (0.36 mol + 1.00 mol + 1.00 mol) [since 1 mol of ethane yields 1 mol of ethene and 1 mol of hydrogen]
P(C2H4) = 0.36 mol / 2.36 mol
P(C2H4) = 0.152
Similarly, we can find the partial pressure of hydrogen gas (H2):
P(H2) = 0.36 mol / 2.36 mol
P(H2) = 0.152
Finally, we can calculate the value of Kp by substituting the calculated partial pressures into the formula:
Kp = (0.152 * 0.152) / (180kPa)
After calculating, we get the following value for Kp at 1000K.