THE CONVERSION RATIOS

There is a conversion factor for going from ##”mm Hg”## (or ##”torr”##) to ##”atm”##:

##mathbf(“1 atm” = “760 mm Hg” = “760 torr”)##

There also exists a conversion factor for ##”PSI”##. I actually don’t know it, so I looked it up: https://www.google.com/?gws_rd=sslq=psi+to+torr

Turns out it’s ##mathbf(“51.7149 torr = 1 PSI”)##.

(Google is a great resource. You should practice with it!)

PERFORMING THE CONVERSIONS

(1)

Let’s start from the equality we just wrote out.

##”1 atm”## ##=## ##”760 mm Hg”##

What happens if we divide by ##”1 atm”##? We get the actual ratio for the conversion.

##(1 cancel”atm”)/(1 cancel”atm”)## ##= 1## ##= “760 mm Hg”/”1 atm” = “1 atm”/”760 mm Hg”##

This implies that multiplying by this ratio does NOT change the validity of your answer… only the units. (It preserves your numerical information.)

Thus, we get:

##color(blue)(P_”atm”) = 255 cancel”mm Hg” xx “1 atm”/(760 cancel”mm Hg”)##

##=## ##color(blue)(“0.336 atm”)##

So now you have the same pressure in different units.

(2)

Like before, we have a ratio that is equal to ##1##:

##1 = “51.7149 torr”/”1 PSI” = “1 PSI”/”51.7149 torr”##

This ratio is used as follows:

##color(blue)(P_”torr”) = 620 cancel”torr” xx “1 PSI”/(51.7149 cancel”torr”)##

##=## ##color(blue)(“12.0 torr”)##

Again, the same pressure as ##”620 torr”##, but in different units.