Final answer:
The pressure in the arm in contact with the gas is -94.48 mm.
Step-by-step explanation:
The pressure of the gas in the open-ended arm of the manometer can be determined by subtracting the atmospheric pressure from the total pressure. First, convert the pressure of the gas to torr by multiplying the given pressure of 0.340 atm by 760 torr/atm. This gives a pressure of 258.4 torr. Then, subtract the atmospheric pressure of 809 torr from the pressure of the gas to find the pressure in the open-ended arm: 258.4 torr - 809 torr = -550.6 torr. Since pressure is a positive value, the negative sign indicates that the pressure in the open-ended arm is lower than atmospheric pressure.
To find the height of the mercury in the arm in contact with the gas, we can use a proportion. The pressure exerted by a fluid due to gravity is known as hydrostatic pressure, which is given by the equation P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column.
Since the density of mercury is about 13.6 times greater than water, we can use the same equation but with the density of mercury instead. Since we are given the height of the mercury in the open-ended arm (69 mm), we can plug in the values and solve for the height of the mercury in the arm in contact with the gas:
Pressure in the open-ended arm / Atmospheric pressure = Height in the open-ended arm / Height in the arm in contact with the gas
-550.6 torr / 760 torr = 69 mm / x
Solving for x, we get:
x = (69 mm) * (760 torr) / (-550.6 torr) = -94.48 mm
The height of the mercury in the arm in contact with the gas is approximately -94.48 mm.