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

Oct 30, 2016

$\text{5.28 atm}$

#### Explanation:

Your task here is to convert from kilopascals, $\text{kPa}$, to atmospheres, $\text{atm}$, by using a conversion factor.

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

${\text{1 Pa" = "1 N"/"1 m}}^{2}$

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

$\text{101325 N"/"1 m"^2 = "101325 Pa}$

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

$\text{1 atm " = " 101325 Pa}$

Since you know that

$\text{1 kPa" = 10^3"Pa}$

you can say that you have

$\textcolor{p u r p \le}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{1 atm " = " 101.325 kPa}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

This is your conversion factor. You can use it to say that the pressure at $\text{45.0 m}$ 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.