A Snowy Globe

Chemistry Level 2

How many water $(\text{H}_{2}\text{O})$ molecules are in a fist-size snowball? Give your answer as the order of magnitude .

The answer is 25.

1 solution

Felipe Hofmann
Aug 8, 2014

A fist-size snowball has aproximately $200mL$ . Because density of snow is $0.9g/cm^3$ , we have $180g = 10 mol$ of water.

Avogadro's number is $6\times10^{23}$ , so 10 mol is $6\times 10^{24}$ water molecules, which has an order of magnitude of $\boxed{25}$ .

A quesion: does Brilliant have chemistry problems?

Gosh! I thought it has ice molecules, not water ones, and consequently answered 0. And yes, there's a chemistry section in Brilliant, and so are problems, although there's no rating and leveling system yet.

Satvik Golechha - 6 years, 10 months ago

Ice is a solid phase transition of H2O. Most people would call water molecules by default.

Steven Zheng - 6 years, 10 months ago

Your answer actually has an order of magnitude of 24. Close enough, I guess.

Steven Zheng - 6 years, 10 months ago

I think we consider the GIF of the base 10 logarithm, which is 25.

Satvik Golechha - 6 years, 10 months ago

No. Order of magnitude is the number to which 10 is elevated. For example, $6\times 10^{24}=10^{24.78}$ , and we aproximate it to 25. For a number between 0 and 10, we say it has order of magnitude of 1 if it is greater than $10^{1/2}=3.16$ .

Felipe Hofmann - 6 years, 10 months ago

A Snowy Globe

The answer is 25.

1 solution

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