Relationship between torr and height?

[SonhosDaVida]

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In this question, why does a height difference of 317 mm correspond to a pressure difference of 317 torr? I know prrsspre and height are proportionally related, but I didn't think they were the same number.

Does this also mean that a height difference of 317 mm equals a pressure difference of 317 atm?

 

[SonhosDaVida]

Pic below

 

[AdaptPrep]

Hi, SonhosDaVida,

Two pressures are acting on the mercury: the pressure of the open end which is atmospheric pressure and the pressure of the gas enclosed in the closed end. The atmospheric pressure will push the mercury down in the open end of the column while the gas enclosed will push the mercury down in the closed end of the column. Therefore, delta h is the difference in pressures (in mm Hg or torr). In this case, a height of 317 mm Hg is a pressure difference of 317 torr because 1 mm Hg = 1 torr. (you can just as well say that 317 mm Hg is the pressure difference)

However, 317 mm Hg does not equal 317 atm because:
1 mm Hg = 1 torr
760 torr = 760 mm Hg = 1 atm

Set up an equation so units cancel:

317 mm Hg * (1 atm / 760 mm Hg) = 0.417 atm (divide 317 by 760)

If you have less than 760 mm Hg, you have less than 1 atm.

I hope that answers your question.

Happy Studying!