How to Calculate Total Pressure in a Container

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You can calculate the total pressure of a given amount of gas present in a container using the Ideal Gas Law. Because gases, unlike solids and liquids, have neither fixed shape nor fixed volume, you can take it that the volume of a gas equals the given or calculated volume of the container. Containers of gases should have no holes and should remain tightly corked to prevent the gas from diffusing through the holes. In standard SI units, pressure is measured in pascal (Pa). However, you can use other common units including the atmosphere (atm).

Things You'll Need

  • Calculator
  • Define the parameters you will need. The Ideal Gas Law you will use states that the total pressure (P) in atmosphere equals the number of moles of the gas (n) in moles times molar gas constant (R) in liter atmospheres per mole per Kelvin times temperature (T) in Kelvin divided by volume (V) in liters. Therefore, you will need four parameters: "n", "R", "T", and "V".

  • Calculate the number of moles. Some chemistry problems that involve calculating the total pressure of a gas in a container will require you to calculate the number of moles first. If you need to calculate the number of moles, then continue with this step, otherwise go to the next step. If you know the mass of the gas, divide it by the molar mass on a calculator and the result is "n". If you know the number of molecules, divide it by Avogadro's number on a calculator and the result is "n". If you know the volume of the gas at Standard Temperature and Pressure (STP), divide it by the molar volume at STP on a calculator and the result is "n".

  • Calculate the volume of the gas. Some chemistry problems that involve calculating the total pressure of a gas in a container will require you to calculate the volume of the gas first. If you need to calculate the volume of gas, which is equivalent to the volume of the container, then continue with this step, otherwise go to the next step. If the container is a cylinder and you know the radius in meters and height in meters, calculate 3.1 times radius squared times height on a calculator and the result is "V" in meters cubed. Then multiply the result by 1000 on your calculator; you'll obtain the result in liters. If the container is a sphere and you know the radius in meters, calculate 1.3 times 3.1 times radius cubed on your calculator. The result is volume of the gas in meters cubed. To convert the result to liters, multiply the result by 1000 on your calculator. If the container is a rectangle and you know the length, width and height in meters, calculate length times width times height on your calculator. The result is volume of gas in meters cubed. To convert the result to liters, multiply the result by 1000 on your calculator.

  • Perform the calculation. Calculate "n" times 0.082058 times "T" divided by "V" with the aid of a calculator to obtain "P" in atmospheres. The value for "P" is the total pressure of the gas in the container.

Tips & Warnings

  • Useful pressure converters include:
  • 1 pascal (Pa) equals 1 N*m-2 equals 1 kg*m-1*s-2
  • 1 atmosphere (atm) equals 1.01325*105 Pa
  • 1 atmosphere (atm) equals 760 torr
  • 1 bar equals 105 Pa
  • The value for the molar gas constant (R) is 0.082058 L atm mol-1 K-1.
  • Temperature equivalence in Kelvin (T) of t degree Celsius is T = 273 + t
  • Number of moles of a gas is the ratio of given mass divided by molecular mass of the gas
  • At standard temperature: 0°C = 273.15 K
  • Standard volume of 1 mole of an ideal gas at STP equals 22.4 liters
  • The Ideal Gas Law is used to solve problems regarding only gases of one substance, i.e., pure gases. When several substances are mixed in one container, use the Ideal Gas Law to determine the pressure of each substance, partial pressure, then use Dalton's law of partial pressures to determine the total pressure of the mixture in the container. Dalton's law of partial pressures states that the total pressure exerted on a container by several different gases equal the sum of the pressures exerted on the container by each gas.

References

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