Calculating Mass and Height of Ideal Gas in a Vertical Tank

In summary, the problem involves a vertical cylindrical tank containing 1.75 moles of an ideal gas at a pressure of 1.00 atm and a temperature of 20.0 degrees Celsius. The tank has a radius of 10.0 meters and is supporting a piston without friction. The first question asks for the mass of the piston, while the second question asks for the height of the column of gas supporting the piston. Using the ideal gas law (PV = nRT), the height is calculated to be 1.34 meters. However, the mass of the piston cannot be determined without units for the given values.
  • #1
pyroknife
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Homework Statement



A vertical cylindrical tank contains 1.75 of an ideal gas under a pressure of 1.00 at 20.0. The round part of the tank has a radius of 10.0 , and the gas is supporting a piston that can move up and down in the cylinder without friction.
What is the mass of this piston?
How tall is the column of gas that is supporting the piston?

Homework Equations



pv=nrt

The Attempt at a Solution

for the 2nd question i got h=1.34m and that answer is correct. I have no clue how to find the mass of the piston using pv=nrt.
 
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  • #2
I see your problem. You gave no units to work with.
 

FAQ: Calculating Mass and Height of Ideal Gas in a Vertical Tank

What is the formula for finding mass using pv=nrt?

The formula for finding mass using pv=nrt is mass = (pressure x volume) / (gas constant x temperature).

What are the units of measurement for each variable in the formula?

The units of measurement for mass are typically grams (g), pressure is measured in Pascals (Pa), volume in cubic meters (m^3), temperature in Kelvin (K), and the gas constant is typically given in units of joules per mole Kelvin (J/mol·K).

3. How is this formula derived?

This formula is derived from the ideal gas law, which states that the product of pressure and volume is directly proportional to the number of moles of gas and the temperature. By rearranging the equation to solve for mass, we can derive the formula mass = (pressure x volume) / (gas constant x temperature).

4. Can this formula be used for all gases?

Yes, this formula can be used for all gases as long as the units of measurement are consistent. However, it is important to note that the gas constant (R) may vary depending on the units used for pressure, volume, and temperature.

5. What are some practical applications of using this formula?

This formula is commonly used in chemistry and physics experiments to calculate the mass of a gas. It is also used in the field of engineering for designing and analyzing systems that involve gases, such as HVAC systems and gas storage tanks. Additionally, this formula is used in industries such as food and beverage production to determine the amount of gas needed for carbonation.

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