Question

How do you convert `"255 mm Hg"` to `"atm"`? What about `"620 torr"` to `"PSI"`?

Answer 1

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=ssl#q=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 PSI")`

Again, the same pressure as `"620 torr"`, but in different units.