Density of Gases



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How to Measure Density of Gases

Three Methods:

Density is defined as the amount of mass present in a given volume. For solids and liquids, this is a fairly straightforward measurement. However, gases are extremely responsive to temperature and pressure (more so than solids or liquids), which can cause their densities to change rather quickly. If you are determining density experimentally, you will have to account for this temperature and pressure sensitivity. If you intend to find the theoretical density of a gas, you will need to utilize the Ideal Gas Law to account for all variables.

Steps

Determining the Density of Gas Experimentally

  1. Fill a balloon.A balloon is designed to be inflated by gas, which makes it the perfect vessel for you to store a fixed amount of gas. You can fill the balloon with air using a pump, or you can choose another type of gas such as helium or nitrogen. Once the balloon is filled, tie off the end so that no gas escapes.
  2. Submerge the balloon completely in a clear container.Next, submerge the balloon in a container of water. The balloon will cause the water level to rise. Mark the new height of the water and remove the balloon.
  3. Measure the amount of displaced water.Use a measuring instrument (e.g., a cup or beaker) to measure the amount of water needed to fill the container to the mark (without the balloon in the water). Pour slowly. If you pour too much, you will have to start over. The volume of the balloon is equal to the volume of the water you add. Record this value for later use as V.
    • You can save time by submerging the balloon into a large beaker or other pre-measured container. Then you can skip adding any water and simply subtract the volume of the water from the volume of the water and balloon.
  4. Weigh the gas filled balloon.You can weigh the balloon using a sensitive scale. Electric scales are usually the best for this application. Record the weight of the gas filled balloon for later use as mGB.
    • If you are filling the balloon with a gas that is lighter than air, you will need to weigh the take before and after you fill the balloon to determine the amount of gas used.
  5. Find the mass of the empty balloon.Poke a hole in the balloon. This will allow the gas to escape. Weigh the balloon again and record the weight of the empty balloon as mB.
  6. Do the calculations.Now that you have enough data, you can calculate the density of the gas inside the balloon. Subtract the weight of the empty balloon, mB, from the weight of the full balloon, mGB. This will give you the mass of the gas alone, mG. Divide the mass of the gas, mG, by the volume, V, of the gas to find the density of the gas, DG.
    • mGB- mB= mG
      • For example, if the full balloon had a mass of 1 kg and the empty balloon had a mass of 0.5 kg, the mass of the gas (mG) would be found by: 1 kg - 0.5 kg = 0.5 kg.
    • mG/ V = DG
      • For example, if the balloon displaced 1 L of water, the density could be found by dividing the mass by that volume: 500 g / 1 L = 500g/L

Finding the Theoretical Density of a Gas

  1. Understand the Ideal Gas Law.You should know that the Ideal Gas Law is a theoretical tool that governs the behavior of gases under specific conditions. You can summarize it in the equation PV=nRT. This simply means that pressure (P) multiplied by volume (V) is equal to the number of moles (n) times the Ideal Gas Constant (R) times the absolute temperature (T) for an ideal gas.
    • A mole (n) is equal to 6.022*10^23 molecules of gas.
    • The Ideal Gas Constant (R) is 0.0821 L·atm/mol·K.
    • Absolute temperature is measured in Kelvins (K).
  2. Assume standard temperature and pressure.Standard temperature and pressure, or STP, is defined as 273 K (32 °F) ( 0 °C) and 1 standard atmosphere (1.0 bar). Assuming STP allows you to calculate the volume of 1 mole of any gas to be 22.414 liters. Knowing this volume will be imperative to finding the density of your gas.
  3. Find the molar mass of the gas.Since you are using STP and assuming one mole of gas, the finding the molar mass will be easy. Add the molar mass of all of the individual atoms that make up you gas to find the molar mass of the gas. The atomic masses can be found on the periodic table.
    • For example, finding the molar mass of H2O gas would mean adding the masses of 2 hydrogens and 1 oxygen. The resulting molar mass would be 18 g/mol (1 g/mol + 1 g/mol + 16 g/mol).
  4. Calculate the density of the gas.Though the volume and moles of gas are fixed in these calculations, the molar mass is different for every gas. That means that the density will be different for each gas as well. To find a given gas density, divide the molar mass of the gas by the molar volume (22.4 L / mol in this case).
    • For example, if you were looking for the density of water vapor, you would divide 18 g/mol by 22.4 L/mol to yield 0.804 g/L. That is: 18 g/mol / 22.4 L/mol = 0.804 g/L.

Finding the Theoretical Density of a Gas Mixture

  1. Know the fractional breakdown of the gas mixture.If you have mixed two or more gases, you will need to know how much of each gas is present. This is done on a percent basis. That allows you to know the ratios of the mixture regardless of how much gas is present overall.
    • For example, if you had a mixture of 75% CO2(carbon dioxide) and 25% H2O (water), those ratios would not change whether you have 1 L or 1,000 L of gas.
  2. Find the mass of one mole.By knowing the ratio of your gases, you can find the molar mass of your mixture. You will have to find the molar mass of each gas, and multiply it by its percent composition in the mixture. Then, add all of the products together to find the molar mass of the gas mixture.
    • For example, you would find the molar mass of CO2(44 g/mol) and multiply it by 0.75. Next you would find the molar mass of H2O (18 g/mol) and multiply it by 0.25. When you add these products together, 33 g/mol + 4.5 g/mol, you yield the molar mass of your mixture. In this case, the molar mass is 37.5 g/mol.
  3. Divide by the volume.Once the molar mass has been established for your mixture, finding the density of the gas is a simple calculation. Divide the molar mass by the standard volume (22.4 L/mol). Remember that you are assuming STP and 1 mole of gas.
    • For example, the density of a mixture of 75% carbon dioxide and 25% water would be37.5g/mol/22.4L/mol=1.67g/L{\displaystyle 37.5g/mol/22.4L/mol=1.67g/L}.
    • You must apply the Ideal Gas Law formula for your calculations if the gas is not at STP (PV=nRT).

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  • Double check all calculations before proceeding to the next one.
  • Remember that the theoretical calculations make strict assumptions about the conditions of the gas.
  • You need only memorize one formula: PV=nRT. You can use a variation of the same formula to find other properties. For instance, to find the volume, use V = nRT/P.

Warnings

  • With basic equipment, the measuring the density of gas is likely to have significant error. This is okay for academic applications, but should be taken into account for applications that require more precise results (e.g. industrial applications).





Video: Gas Density and Molar Mass Formula, Examples, and Practice Problems

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Date: 12.12.2018, 21:51 / Views: 35254