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 585-mm column of di-n-butyl phthalate. The density of mercury is 13.53 g·mL–1.
585 mm x (1.046/13.53) = ?
To compute the pressure, we need to use the equation for pressure:
Pressure = Density × Gravity × Height
First, let's convert the height of the column from millimeters to centimeters:
585 mm = 58.5 cm
Next, we need to convert the density of di-n-butyl phthalate from grams per milliliter (g·mL–1) to grams per cubic centimeter (g·cm–3):
1.046 g·mL–1 = 1.046 g·cm–3
Since the density of mercury is given in g·mL–1, we can directly use it.
Now, let's substitute the values into the pressure formula:
Pressure = (1.046 g·cm–3 - 13.53 g·mL–1) × 9.8 m/s^2 × 58.5 cm
Before we continue, we need to convert the density difference from g·mL–1 to g·cm–3:
13.53 g·mL–1 = 13.53 g·cm–3
Now, we can calculate the pressure:
Pressure = (1.046 g·cm–3 - 13.53 g·cm–3) × 9.8 m/s^2 × 58.5 cm
Simplifying the equation further:
Pressure = (-12.484 g·cm–3) × 9.8 m/s^2 × 58.5 cm
Pressure = -7258.8 g·cm^2/s^2
To convert the unit to torr, we'll use the conversion factor:
1 torr = 133.3224 g·cm^2/s^2
Pressure = -7258.8 g·cm^2/s^2 × (1 torr / 133.3224 g·cm^2/s^2)
Pressure ≈ -54.49 torr
Since pressure cannot be negative, we can conclude that the pressure of the gas supporting the column of di-n-butyl phthalate is approximately 54.49 torr.