If the pressure is 748 mmHg, and if h= 35mm, what is the pressure of the gas, expressed in atm, If the substance in the tube is oil having a density of 0.788 g/mL? The density of mercury is 13.6 g/mL.
I don't think your post is clear. I don't know what you're asking. It appears to me that if the pressure is 748 mm Hg then the pressure is 748/760 = ? atm and I know that isn't what you're asking.
To find the pressure of the gas in atm, we need to consider the relationship between pressure, height, and density of the liquid column. Let's break down the problem step by step.
1. Calculate the pressure due to the oil column:
The pressure due to the oil column can be found using the equation:
Pressure = (density of oil) * (gravity) * (height of oil column)
Given:
Density of oil = 0.788 g/mL = 0.788 g/cm^3
Height of oil column (h) = 35 mm
First, convert the height from millimeters to centimeters:
Height of oil column (h) = 35 mm = 3.5 cm
Next, plug in the values into the equation:
Pressure due to oil column = (0.788 g/cm^3) * (9.8 m/s^2) * (3.5 cm)
= 26.47 g/cm^2/s^2
2. Convert the pressure due to the oil column to atm:
Since mercury is commonly used in pressure measurements, we need to convert the pressure from g/cm^2/s^2 to atm. We can use the density of mercury to determine the conversion factor.
Given:
Density of mercury = 13.6 g/mL = 13.6 g/cm^3
Convert the pressure due to the oil column from g/cm^2/s^2 to atm:
Pressure due to oil column (atm) = (Pressure due to oil column) / (density of mercury)
Plug in the values:
Pressure due to oil column (atm) = 26.47 g/cm^2/s^2 / 13.6 g/cm^3
≈ 1.946 atm (rounded to three decimal places)
3. Calculate the total pressure of the gas:
The total pressure of the gas is the sum of the pressure due to the oil column and the given pressure.
Given:
Pressure = 748 mmHg
Convert the given pressure from mmHg to atm:
Pressure (atm) = 748 mmHg / 760 mmHg/atm
≈ 0.984 atm (rounded to three decimal places)
Calculate the total pressure:
Total pressure (atm) = Pressure (atm) + Pressure due to oil column (atm)
= 0.984 atm + 1.946 atm
≈ 2.93 atm (rounded to two decimal places)
Therefore, the pressure of the gas, expressed in atm, is approximately 2.93 atm.