A gas sample is connected to an open-end manometer. The mercury level is 25 mm lower in the side open to the atmosphere, and the atmospheric pressure is 754 torr. What is the pressure of the gas?
To find the pressure of the gas in the system, we can make use of the fact that the difference in mercury levels in a manometer is directly related to the pressure difference between the gas and the atmosphere.
In this case, we are given that the mercury level is 25 mm lower in the side open to the atmosphere. Let's call this difference in height "h". So, h = 25 mm.
We are also given that the atmospheric pressure is 754 torr.
Now, let's consider the two sides of the manometer:
1. The side connected to the gas: The height of the mercury column in this side is zero because it is open to the gas sample.
2. The side open to the atmosphere: The height of the mercury column in this side is h = 25 mm.
Since the pressure of the gas in the system is related to the height difference, we can express the pressure of the gas as:
Pressure of gas = Atmospheric pressure + h
Plugging in the given values, we have:
Pressure of gas = 754 torr + 25 mm
However, we need to convert the height from mm to torr in order to ensure consistent units. To do this, we can use the fact that 1 mm of mercury is equivalent to 1 torr.
So, 25 mm = 25 torr.
Now we can substitute this value into our equation:
Pressure of gas = 754 torr + 25 torr
Therefore, the pressure of the gas is 779 torr.