Following this pair of tweets about water:

A bucket full of water contains more atoms than there are bucketfuls of water in the Atlantic Ocean

— The QI Elves (@qikipedia) February 5, 2012

.@qikipedia There are 10,000× more molecules per pint of water than pints of water on earth. (3×10^21 pints/earth vs 2×10^25 molecules/pint)

— Matt Parker (@standupmaths) February 5, 2012

The obvious question is, at what point are the two numbers the same? Or,

If you put all the Earth’s water into containers of the same size so that each container carries as many atoms of water as there are containers, how big is each container?

Facts

• Atoms in $1l$ of water: $1\times {10}^{26}$
• Total water on earth: $1.386\times {10}^{21}l$

Working

We want this equation to hold:

$$\text{atoms in }1l\text{ of water}\times \text{volume of container}=\frac{\text{litres of water on Earth}}{\text{volume of container}}$$

Rearrange that to get an expression for the volume of the container:

$$\begin{array}{rl}\text{volume of container}& =\sqrt{\frac{\text{litres of water on Earth}}{\text{atoms in }1l\text{ of water}}}\\ & =\sqrt{\frac{1.386\times {10}^{21}}{1\times {10}^{26}}}\\ & =\sqrt{1.386\times {10}^{-5}}\\ & =0.00372290209l\\ & \approx 3.723ml\end{array}$$

Conclusion

The container is really, really tiny — just over half a teaspoon!