Solution:

To find the approximate value of x y / x-y for 109% labelled oleum, we need to first understand the concept of oleum and its composition.

Oleum:
Oleum is a highly concentrated form of sulfuric acid (H2SO4). It is commonly known as fuming sulfuric acid or Nordhausen acid. Oleum is formed by dissolving sulfur trioxide (SO3) in sulfuric acid.

Composition of Oleum:
Oleum is represented by the formula H2SO4.xSO3, where x represents the amount of free SO3 present in the oleum. The value of x can vary depending on the concentration of the oleum.

Given Information:
In this case, we have 109% labelled oleum. This means that the oleum contains 109% of the required amount of SO3. Let's assume the number of moles of H2SO4 to be x and the number of moles of free SO3 to be y.

Calculating the Moles of H2SO4 and SO3:
Since oleum is a concentrated form of sulfuric acid, we can assume that the number of moles of H2SO4 is equal to the number of moles of SO3. Therefore, x = y.

Approximating x y / x-y:
We need to calculate the value of x y / x-y, which can be done as follows:

x y / x-y = (x * x) / (x - x)

As x and y are equal, the above expression simplifies to:

x y / x-y = (x * x) / 0

Since the denominator is zero, the value of x y / x-y is undefined.

Explanation:
The approximate value of x y / x-y for 109% labelled oleum is undefined because the number of moles of H2SO4 and free SO3 in oleum are assumed to be equal. If we assume any value for x and y, the denominator of the expression becomes zero, resulting in an undefined value.

Therefore, the approximate value of x y / x-y for 109% labelled oleum cannot be determined.

Conclusion:
The approximate value of x y / x-y for 109% labelled oleum is undefined. This is because the number of moles of H2SO4 and free SO3 in oleum are assumed to be equal, resulting in a zero denominator.