Question 90540

Aug 4, 2017

Answer:

$60$ $\text{mol H"_2"O}$ ($1$ 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 $1$ ${\text{g/cm}}^{3}$ is equivalent to $1$ $\text{g/mL}$, 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 $1$ $\text{L H"_2"O}$ 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 ($18.015$ $\text{g/mol}$) to calculate the number of moles:

$\textcolor{g r e e n}{{10}^{3}} \cancel{\textcolor{g r e e n}{\text{g H"_2"O"))((1color(white)(l)"mol H"_2"O")/(18.015cancel("g H"_2"O"))) = color(blue)(ulbar(|stackrel(" ")(" "60color(white)(l)"mol H"_2"O"" }} |}$

rounded to $1$ significant figure.