A column of mercury in a barometer is 767.3 mm Hg high. Note, that in order for the pressures to be equal, density and height of a column are inversely proportional, therefore, (den1)(h1)=(den2)(h2). The density of mercury is 13.6 g/mL and the density of water is 1.00g/mL.
a) How high would that column be if it were water instead of mercury?
Why can't you simply substitute into the formula given in the problem?
To find the height of the water column, we can use the formula for the relationship between the density and height of two columns of different fluids in a barometer.
The formula is:
(den1)(h1) = (den2)(h2)
Given:
The height of the mercury column, h1 = 767.3 mm Hg
The density of mercury, den1 = 13.6 g/mL
The density of water, den2 = 1.00 g/mL
We need to find h2, which is the height of the water column.
Using the formula mentioned earlier, we can rearrange it to solve for h2:
h2 = (den1)(h1) / den2
Plugging in the values we have:
h2 = (13.6 g/mL)(767.3 mm Hg) / 1.00 g/mL
To cancel out the units, we can convert the height of the mercury column from mm Hg to mL:
1 mm Hg = 1 mL
Now, let's calculate:
h2 = (13.6 g/mL)(767.3 mL) / 1.00 g/mL
h2 = 10438.08 mL
Therefore, the height of the water column would be 10438.08 mL.