No, there is not a mole of water molecules on Earth. There are vastly more than a mole of water molecules on Earth. Here's why:

* A mole is a huge number: One mole is equal to 6.022 x 10^23 (Avogadro's number) of anything, be it atoms, molecules, or other particles.

* Earth's oceans are vast: The Earth's oceans contain an enormous amount of water, estimated to be around 1.332 x 10^21 kg.

* Water's molecular weight: The molecular weight of water (H2O) is approximately 18 g/mol.

Calculation:

1. Mass of water in grams: 1.332 x 10^21 kg * 1000 g/kg = 1.332 x 10^24 g

2. Moles of water: (1.332 x 10^24 g) / (18 g/mol) = 7.4 x 10^22 mol

Conclusion:

The Earth's oceans contain approximately 7.4 x 10^22 moles of water molecules, which is significantly larger than just one mole.