PROBLEM 122P
Consider the reaction:
CO(g) + 2H2(g) → CH3OH(g)
A reaction flask initially contains 112 torr of CO and 282 torr of H2. The reaction is allowed to proceed until the pressure stops changing, at which point the total pressure is 196 torr. Determine the percent yield for the reaction. Assume a constant temperature and that no other reactions occur other than the one indicated.
Solution 122
Here, we are going to determine the percent yield for the given reaction.
Step 1:
The given reaction is:
CO(g) + 2H2(g) → CH3OH(g)
From the above equation, it is clear that 1 mole of CO requires 2 moles of H2 for complete reaction.
Now, at constant temperature and volume, the pressure(p) of a gas is directly proportional to the number of moles(n).
Thus,
p ∝ n
Now, if p1, n1 are the pressure and number of moles of a gas and p2, n2 are the volume and number of moles of another gas , then,
p1 = kn1
p2 = kn2
Combining the two equations, we get, p1 / n1 = p2 / n2 -----(1)
Step 2:
Let, p1, n1 are the pressure and number of moles of CO and p2, n2 are the volume and number of moles of H2 , then, pressure of H2 required to react with 112 torr pressure of CO is given by:
p2 = (p1 x n2) / n1
= (112 torr x 2 mol) / 1 mol
= 224 torr
But we have H2 at 282 torr pressure, i.e., the pressure of H2 is in excess. Thus, CO acts as a limiting reactant.
