# Question #c46c3

##### 1 Answer

#### Explanation:

The idea here is that you need to use a series of conversion factors to get you from quarts per seconds to quarts per year.

Once you do that, convert the quarts to liters and use water's density to calculate the mass in kilograms of that volume of water.

So, the conversion factors that can take you from quarts per seconds to quarts per year are

#1"qt"/color(red)(cancel(color(black)("s"))) * (60color(red)(cancel(color(black)("s"))))/(1color(red)(cancel(color(black)("min")))) * (60color(red)(cancel(color(black)("min"))))/(1color(red)(cancel(color(black)("h")))) * (24color(red)(cancel(color(black)("h"))))/(1color(red)(cancel(color(black)("day")))) * (365.25color(red)(cancel(color(black)("days"))))/"1 year" = "31,557,600" "qt"/"year"#

This means that a rate of

#5.890 * underbrace("31,557,600" "qt"/"year")_(color(blue)(=1 "qt"/"s")) = "185,874,264" "qt"/"year"#

In exactly one year, the room will contain

Convert this volume to liters by using the fact that

#"185,874,264"color(red)(cancel(color(black)("qt"))) * "1 L"/(1.05668821color(red)(cancel(color(black)("qt")))) = "175,902,657.2 L"#

At

#"175,902,657.2"color(red)(cancel(color(black)("L"))) * "998.039 kg"/(1color(red)(cancel(color(black)("L")))) = color(green)(1.756 * 10^11"kg")#

of water. The answer is rounded to four sig figs.