# What is the equivalent pressure of 0.743 atm in units of mm Hg?

Jul 18, 2016

$\text{565 mmHg}$

#### Explanation:

The problem wants you to use a known conversion factor to go from pressure expressed in atmospheres, $\text{atm}$, to pressure expressed in millimeter of mercury, $\text{mmHg}$.

Now, you can find the conversion factor that takes you from atmospheres to millimeter of mercury by using the pascals, $\text{Pa}$, the SI unit of pressure.

In terms of pascals, an atmosphere is defined as a pressure of

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

Similarly, a millimeter of mercury, which is simply the pressure exerted by a $\text{1-mm}$ high column of mercury, is defined as a pressure of approximately

$\text{1 mmHg " ~~ " 133.32239 Pa}$.

Your goal now is to find how many milliliters of mercury are needed to get to the equivalent of one atmosphere. You can say that you have

overbrace(101325 color(red)(cancel(color(black)("Pa"))))^(color(blue)("= 1 atm")) * "1 mmHg"/(133.32239color(red)(cancel(color(black)("Pa")))) ~~ "760 mmHg"

This tells you that a column of mercury $\text{760 mm}$ high creates a pressure equal to $\text{1 atm}$. You can thus say that your conversion factor looks like this

$\textcolor{p u r p \le}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{1 atm " = " 760 mmHg}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Use this conversion factor to find the equivalent pressure of $\text{0.743 atm}$ in units of $\text{mmHg}$

0.743 color(red)(cancel(color(black)("atm"))) * "760 mmHg"/(1color(red)(cancel(color(black)("atm")))) = color(green)(|bar(ul(color(white)(a/a)color(black)("565 mmHg")color(white)(a/a)|)))

The answer is rounded to three sig figs.