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The volume occupied by one mole of an ideal gas at 273 K and 1.01×105 Pa is 22.4 dm3. What volume, in dm3, is occupied by 3.20 g O2(g) at 273 K and 1.01×105 Pa?

Question

The volume occupied by one mole of an ideal gas at 273 K and 1.01×105 Pa is 22.4 dm3. What volume, in dm3, is occupied by 3.20 g O2(g) at 273 K and 1.01×105 Pa?

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Solution

To solve this problem, we need to use the ideal gas law and the molar mass of oxygen. Here are the steps:

  1. First, we need to find the number of moles of O2. The molar mass of O2 is approximately 32.00 g/mol (since the atomic mass of oxygen is approximately 16.00 g/mol and O2 has two oxygen atoms). So, we can calculate the number of moles by dividing the mass of O2 by its molar mass:

    Number of moles = mass / molar mass = 3.20 g / 32.00 g/mol = 0.1 mol

  2. Next, we use the ideal gas law, which states that the volume of a gas is directly proportional to the number of moles of the gas if the temperature and pressure are held constant. Since we know that one mole of an ideal gas at 273 K and 1.01×105 Pa occupies 22.4 dm3, we can find the volume occupied by 0.1 mol by multiplying the volume of one mole by the number of moles:

    Volume = number of moles * volume of one mole = 0.1 mol * 22.4 dm3/mol = 2.24 dm3

So, 3.20 g of O2(g) at 273 K and 1.01×105 Pa occupies a volume of 2.24 dm3.

This problem has been solved

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