How many moles of hydrogen gas are required to react completely with 807 L of ethylene (C2H4) according to the following reaction at 0oC and 1 atm?
hydrogen (g) + ethylene (C2H4) (g)---> ethane (C2H6) (g)
Should I use the ideal gas law here?
To determine the number of moles of hydrogen gas required to react with ethylene, we can use the ideal gas law. The ideal gas law equation is given by:
PV = nRT
Where:
P = pressure (in atmospheres)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
In this case, we are given the following information:
- The temperature is 0°C, which is equivalent to 273.15 Kelvin.
- The pressure is given as 1 atm.
- The volume of ethylene is given as 807 L.
However, we want to find the number of moles of hydrogen gas, not ethylene. To do this, we need to use the stoichiometry of the reaction, which tells us the mole ratio between the reactants and products. From the balanced chemical equation:
hydrogen (g) + ethylene (C2H4) (g) ---> ethane (C2H6) (g)
The balanced equation tells us that for every 1 mole of hydrogen gas (H2), 1 mole of ethylene (C2H4) is consumed.
So, to find the number of moles of hydrogen gas, we will use the following steps:
Step 1: Convert the temperature to Kelvin.
0°C + 273.15 = 273.15 K
Step 2: Plug the values into the ideal gas law equation.
PV = nRT
(1 atm) * (807 L) = n * (0.0821 L·atm/mol·K) * (273.15 K)
807 atm·L = 22.4147 n
Step 3: Solve for the number of moles (n).
n = (807 atm·L) / (22.4147 L/mol)
n ≈ 36.03 moles
Therefore, approximately 36.03 moles of hydrogen gas are required to react completely with 807 L of ethylene.