Liquid methylene iodide has a density of 3.33 g/mL. A barometer is constructed using methylene iodide instead of mercury. If the atmospheric pressure is 0.951 atm, what is the height of the methylene iodide column in the barometer in cm?
The density of liquid mercury is 13.6 g/mL
Since the force is the same, the height will be inversely proportional to the densities (because the cross-section has the same area) -- think about it: half as dense (half as much mass), twice as high.
So, if H is the height of mercury, the height h of iodide obeys
h = (13.6/3.33)H
To find the height of the methylene iodide column in the barometer, we can use the equation:
pressure = density * gravity * height
First, let's convert the atmospheric pressure from atm to cmHg.
1 atm is equal to 76 cmHg.
So, 0.951 atm is equal to 0.951 * 76 cmHg, which is equal to 72.276 cmHg.
Now, let's calculate the height of the methylene iodide column:
pressure = density * gravity * height
72.276 cmHg = 3.33 g/mL * 9.8 m/s^2 * height
To make the units consistent, we need to convert g/mL to g/cm^3:
3.33 g/mL is equal to 3.33 g/cm^3
72.276 cmHg = 3.33 g/cm^3 * 9.8 m/s^2 * height
Next, we need to convert the units of cmHg to cm and m/s^2 to cm/s^2:
1 cmHg is equal to 1.33 cm
1 m/s^2 is equal to 100 cm/s^2
So now, the equation becomes:
72.276 cm = 3.33 g/cm^3 * 100 cm/s^2 * height
Simplifying the equation, we have:
72.276 = 333 g/cm * height
Now, divide both sides of the equation by 333 to solve for the height:
height = 72.276 / 333 cm
Calculating this, we find that the height of the methylene iodide column in the barometer is approximately 0.217 cm.