The organic compound di-n-butyl phthalate, C16H22O4(l), is sometimes used as a low-density (1.046 g·mL–1) manometer fluid. Compute the pressure (in torr) of a gas that supports a 555-mm column of di-n-butyl phthalate. The density of mercury is 13.53 g·mL–1.
Note: For a mercury manometer, the height in millimeters (mmHg) is equal to the pressure in torr. Since the liquid is not mercury, we must use the density ratio to determine what the height would be if it were mercury. The height ratio is the inverse of the density ratio.
I can repeat the hint. The height ratio is the inverse of the density ratio.
What's the density ratio? That will be
(d of 1/d of Hg) = (height Hg/height 1)
(1.046/13.53) = (height Hg/555)
(1.046/13.53) x 555 mm = ?mm.
Why did the organic compound become a manometer fluid? Because it wanted to measure up to the other liquids!
Now, let's get serious and calculate the pressure. We know that the density of di-n-butyl phthalate is 1.046 g·mL–1, and the density of mercury is 13.53 g·mL–1. The height of the column of di-n-butyl phthalate is 555 mm.
To determine the pressure in torr, we need to convert the height of the column of di-n-butyl phthalate to the equivalent height of a mercury column. Luckily, we can use the density ratio to help us with that. The density ratio is the inverse of the height ratio.
So, the height ratio is the density of mercury divided by the density of di-n-butyl phthalate:
Height Ratio = (Density of Mercury) / (Density of di-n-butyl phthalate)
Height Ratio = 13.53 / 1.046
Now, let's use this height ratio to find the equivalent height of the column if it were mercury:
Equivalent Height of Mercury = (Height of di-n-butyl phthalate column) * (Height Ratio)
Equivalent Height of Mercury = 555 * (13.53 / 1.046)
Finally, since the height of the column in millimeters is equal to the pressure in torr for a mercury manometer, we have our answer:
Pressure = Equivalent Height of Mercury = 555 * (13.53 / 1.046) torr
I hope this answer doesn't weigh you down too much!
To solve this problem, we need to calculate the pressure in torr that supports a 555-mm column of di-n-butyl phthalate.
First, we need to determine the density ratio between di-n-butyl phthalate and mercury.
Density ratio = density of di-n-butyl phthalate / density of mercury
Density ratio = 1.046 g/mL / 13.53 g/mL
Now, we can calculate the height in millimeters (mmHg) as if the manometer fluid were mercury.
Height of di-n-butyl phthalate (mmHg) = 555 mm / Density ratio
Finally, we know that the height in millimeters (mmHg) is equal to the pressure in torr. Therefore, the pressure in torr is equal to the height of the di-n-butyl phthalate column.
Pressure in torr = Height of di-n-butyl phthalate (mmHg)
Just substitute the calculated values into the formula to find the pressure in torr.