Question

Question #90540

Answer 1

`60` `"mol H"_2"O"` (`1` significant figure)

Explanation:

We're asked to find the number of moles of water in `1` `L"` water, given its density.

The given density of `1` `"g/cm"^3` is equivalent to `1` `"g/mL"`, which is also equal to

`((1color(white)(l)"g")/(1cancel("mL")))((10^3cancel("mL"))/(1color(white)(l)"L")) = color(red)(ul(10^3color(white)(l)"g/L"`

Now, we can use dimensional analysis to convert from `1` `"L H"_2"O"` to grams:

`1cancel("L H"_2"O")((color(red)(10^3color(white)(l)"g H"_2"O"))/(1cancel("L H"_2"O"))) = color(green)(ul(10^3color(white)(l)"g H"_2"O"`

Lastly, we'll use the molar mass of water (`18.015` `"g/mol"`) to calculate the number of moles:

`color(green)(10^3)cancel(color(green)("g H"_2"O"))((1color(white)(l)"mol H"_2"O")/(18.015cancel("g H"_2"O"))) = color(blue)(ulbar(|stackrel(" ")(" "60color(white)(l)"mol H"_2"O"" ")|)`

rounded to `1` significant figure.