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 determine the pressure of the gas in the manometer, we need to consider the height difference between the two sides of the manometer and the atmospheric pressure.
Given:
Height difference in the manometer (h) = 25 mm
Atmospheric pressure (P_atm) = 754 torr
To get the pressure of the gas (P_gas), we need to calculate the difference in pressure between the two sides of the manometer.
In a manometer, the pressure difference is given by the difference in the heights of the liquid columns. In this case, we have mercury in the manometer, so we will use the difference in mercury levels.
Since the mercury level is lower on the side open to the atmosphere, we can say that the pressure on the gas side is greater than atmospheric pressure. Therefore, the pressure of the gas is given by:
P_gas = P_atm + h
Substituting the values we have:
P_gas = 754 torr + 25 mm
Before we can add these values, we need to convert the height difference from millimeters to torr since the two units are different.
To convert the height difference from millimeters to torr, we can use the conversion factor:
1 torr = 1 mm Hg
So, the height difference in torr is:
h = 25 mm * (1 torr / 1 mm Hg) = 25 torr
Now we can substitute this value into the equation:
P_gas = 754 torr + 25 torr
P_gas = 779 torr
Therefore, the pressure of the gas is 779 torr.