Question

The pressure 45.0 meters under water is 543 kPa. What is this pressure in atm?

Answer 1

`"5.28 atm"`

Explanation:

Your task here is to convert from kilopascals, `"kPa"`, to atmospheres, `"atm"`, by using a conversion factor.

For starters, you should know that the pascal, `"Pa"`, which is the SI unit for pressure, is defined as a force of `"1 N"` pressing down a surface of `"1 m"^2`

`"1 Pa" = "1 N"/"1 m"^2`

At sea level, the molecules of air that make up the atmosphere press down on each square meter with a force of `"101325 N"`, which basically means that at sea level, the atmospheric pressure is equal to

`"101325 N"/"1 m"^2 = "101325 Pa"`

This is also defined as one standard atmosphere, which means that you have

`"1 atm " = " 101325 Pa"`

Since you know that

`"1 kPa" = 10^3"Pa"`

you can say that you have

`color(purple)(bar(ul(|color(white)(a/a)color(black)("1 atm " = " 101.325 kPa")color(white)(a/a)|)))`

This is your conversion factor. You can use it to say that the pressure at `"45.0 m"` below surface level is equal to

`535 color(red)(cancel(color(black)("kPa"))) * "1 atm"/(101.325color(red)(cancel(color(black)("kPa")))) = color(green)(bar(ul(|color(white)(a/a)color(black)("5.28 atm")color(white)(a/a)|)))`

The answer is rounded to three sig figs.