A flask containing a gas was connected to both a closed-end and an open-end manometer. In the closed-end manometer, the mercury in the sealed arm was 755 mm above the level in the arm connected to the fax. In the open-end manometer,the arm connected to the gas was 17 mm higher than the side open to the air. What was the atmospheric pressure in torr?
To find the atmospheric pressure in torr, we need to consider the pressure difference between the closed-end manometer and the open-end manometer.
Let's first consider the closed-end manometer:
The difference in mercury level between the sealed arm and the arm connected to the flask is 755 mm.
Since mercury is a dense liquid, we can assume that a column of mercury is balanced by the atmospheric pressure.
Therefore, the pressure in the flask is equal to the atmospheric pressure plus the pressure due to the column of mercury in the sealed arm.
Now let's consider the open-end manometer:
The difference in mercury level between the arm connected to the gas and the side open to the air is 17 mm.
Since the arm connected to the gas is higher, the pressure in the flask is greater than the atmospheric pressure, and the pressure due to the column of mercury in the gas arm can be thought of as an excess pressure.
Since the pressure due to the column of mercury is directly proportional to the height of the column, we can set up the following equation:
ΔP = Δh × ρ × g
Where:
ΔP = pressure difference between the closed-end and open-end manometers
Δh = height difference in mercury level (closed end - open end)
ρ = density of mercury
g = acceleration due to gravity
Assuming the density of mercury is 13.6 g/cm³ and the acceleration due to gravity is 9.8 m/s², we can convert the 17 mm height difference to cm and calculate the pressure difference:
ΔP = (755 mm - 17 mm) × (13.6 g/cm³) × (9.8 m/s²) = 62444 dyne/cm²
1 dyne/cm² is equal to 1 × 10^-1 torr.
Therefore, the pressure difference is equal to 62444 × 10^-1 torr = 6244.4 torr.
Since the pressure in the flask is equal to the atmospheric pressure plus the pressure difference, we can rewrite the equation as:
Atmospheric Pressure = Pressure in Flask - Pressure Difference
The pressure in the flask, in this case, is equal to the atmospheric pressure plus the pressure due to the column of mercury in the sealed arm:
Pressure in Flask = Atmospheric Pressure + (755 mm × 13.6 g/cm³ × 9.8 m/s²)
Plugging in the values:
Pressure in Flask = Atmospheric Pressure + (755 mm × 13.6 g/cm³ × 9.8 m/s²)
Assuming 1 atm is equal to 760 torr, we can solve for the atmospheric pressure:
Atmospheric Pressure = (Pressure in Flask - Pressure Difference) - (755 mm × 13.6 g/cm³ × 9.8 m/s²)
Atmospheric Pressure = (Pressure in Flask - 6244.4 torr) - (755 mm × 13.6 g/cm³ × 9.8 m/s²)
Finally, we substitute the values and calculate the atmospheric pressure in torr.
To determine the atmospheric pressure in torr, we'll need to analyze the readings from both the closed-end and open-end manometer.
First, let's look at the closed-end manometer. It tells us that the mercury in the sealed arm is 755 mm above the level in the arm connected to the flask. This indicates that the gas pressure inside the flask is greater than the atmospheric pressure outside.
Now, let's consider the open-end manometer. It tells us that the arm connected to the gas is 17 mm higher than the side open to the air. This indicates that the gas pressure inside the flask is less than the atmospheric pressure outside.
To find the atmospheric pressure, we need to find the difference between the gas pressure inside the flask and the atmospheric pressure. This difference can be found by subtracting the readings from the open-end and closed-end manometers.
The equation is as follows:
Difference in Pressure = Height of Sealed Arm - Height of Open Arm
Difference in Pressure = 755 mm - 17 mm
Difference in Pressure = 738 mm
Now we convert the pressure difference from millimeters of mercury (mm) to torr. 1 mm of mercury is equivalent to 1 torr.
Pressure in Torr = Difference in Pressure
Pressure in Torr = 738 torr
Therefore, the atmospheric pressure is 738 torr.