Question fdee5

Sep 22, 2017

$5.41 \cdot {10}^{4}$ $\text{g}$

Explanation:

As you know, the density of a substance tells you the mass of exactly $1$ unit of volume of that substance.

In your case, you know that mercury has a density equal to $\text{13.6 g/mL}$. This tells you that $\text{1 mL}$ of mercury, which represents $1$ unit of volume, will have a mass of $\text{13.6 g}$.

Now, notice that the volume of the sample is given in liters. This means that the first thing that you have to do here is to convert the volume of the sample to milliliters because that is the unit of volume given for the density of mercury.

Use the fact that

$\text{1 L" = 10^3color(white)(.)"mL}$

to get

3.78 color(red)(cancel(color(black)("L"))) * (10^3color(white)(.)"mL")/(1color(red)(cancel(color(black)("L")))) = 3.78 * 10^3color(white)(.)"mL"#

To find the mass of the sample, you need to use the density of mercury as a conversion factor.

Since you have volume and you need mass, set up the mass of $\text{1 mL}$ of mercury as the numerator and the $\text{1 mL}$ of mercury as the denominator.

You will end up with

$3.78 \cdot {10}^{3} \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{mL"))) * "13.6 g"/(1color(red)(cancel(color(black)("mL")))) = color(darkgreen)(ul(color(black)(5.41 * 10^4color(white)(.)"g}}}}$

The answer is rounded to three sig figs.

If you want, you can convert this to kilograms

$5.41 \cdot 10 \cdot \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{{10}^{3}}}} \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{g"))) * "1 kg"/(color(blue)(cancel(color(black)(10^3)))color(red)(cancel(color(black)("g")))) = color(darkgreen)(ul(color(black)("54.1 kg}}}}$