# Question 76833

Sep 29, 2017

$\text{0.56 h}$

#### Explanation:

Start by converting the volume of the vessel from liters to milliliters by using the fact that

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{1 L" = 10^3color(white)(.)"mL}}}}$

In your case, the vessel contains exactly $\text{1.0 L}$ of water, so you can say that it contains $1.0 \cdot {10}^{3}$ $\text{mL}$ of water.

Now, you know that $\text{1.00 mL}$ of water contains $20.0$ drops of water. Use this conversion factor to convert the volume of the vessel from milliliters to drops

1.0 * 10^3 color(red)(cancel(color(black)("mL"))) * "20.0 drops"/(1.00color(red)(cancel(color(black)("mL")))) = 20.0 * 10^3color(white)(.)"drops"

The problem tells you that you can count the drops at a rate of $\text{10.0 drops/s}$, so use this conversion factor to find the total time needed to count all the drops present in the vessel

20.0 * 10^3 color(red)(cancel(color(black)("drops"))) * "1 s"/(10.0color(red)(cancel(color(black)("drops")))) = 2.00 * 10^3color(white)(.)"s"#

Finally, use the fact that

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{1 h = 3600 s}}}}$

to convert the time from seconds to hours.

$2.00 \cdot {10}^{3} \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{s"))) * "1 h"/(3600color(red)(cancel(color(black)("s")))) = color(darkgreen)(ul(color(black)("0.56 h}}}}$

The answer is rounded to two sig figs, the number of sig figs you have for the volume of the vessel.