A gas in a container had a measured pressure of 57 kPa. Calculate the pressure in units of atm and mmHg.
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Pressure is defined as the ratio of a force being applied to an area to the measure of the area. That is P = F/A
There are various value for measuring pressure depending on the units used to measure the force and area. In SI the fundamental unit of pressure is the Pascal which is defined as 1.00 N/m^2 symbolized as Pa. The Pascal is a fairly small measure of pressure, and in many "normal" cases for pressure the unit of measure is commonly the kPa (kiloPascal).
Traditionally, the unit of pressure was the mmHg (millimeter of mercury). This was developed by Alessandro Torricelli who invented the liquid mercury barometer to measure air pressure. In his device he defined the pressure exerted by the atmosphere on a calm day, at sea level, at with a temperature of around 25C is the force required to hold up a column of liquid mercury that is 760 millimeters high. This amount of mercury is called the one atmosphere equivalent. Thus we can define 1.00 atmosphere of pressure as being equal to 760 mmHg.
To honor Torricelli, the mmHg is many times called a Torr. Thus
1.00 atm = 760 mmHg (or 760 Torr)
By converting the height of the mercury column to its mass and weight using the density of mercury and then measuring the area over which the weight of the mercury is supported one can compute the weight per square meter, or N/m^2 of the mercury corresponding to 1.00 atm. This works out to be 101,325 Newtons/m^2 or 101,325 Pa = 101.325 kPa.
With this informatin we can do the assigned conversions:
57kPax(1.00atm/101.325kPa) = 0.563 atm.
57kPax(760mmHg/101.325kPa) = 428 mmHg
of 0.563x(760mmHg/1.00atm) = 428 mmHg.
Converting between units of measurement is easy if you know the appropriate conversion factors.
1.00 atm = 101.33 kPa
1.00 atm = 760. mm Hg = 760. Torr
Using these conversion factors you can muliply and/or divide to get the appropriate answers.
57 kPa * (1.00 atm/101.33 kPa) = 0.56 atm
57 kPa * (760 mm Hg/101.33 kPa) = 430 mm Hg
Keep in mind that when you are performing calculations of these sorts to use the proper number of significant figures. Because the initial value given of 57 kPa only has 2 significant figures, both of your answers should also contain 2 significatn figures, hence the rounding on the second problem.
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