At a certain temperature and pressure, 0.20 mol of carbon dioxide has a volume of 3.1 L. A 3.1-L sample of hydrogen at the same temperature and pressure ____.
I think it's supposed to be "contains the same number of molecules" but I'm not sure.
And there's also this one. I think it's 1/3 also, but I'm not sure.
If the atmospheric pressure on Mt. Everest is one-third the atmospheric pressure at sea level, the partial pressure of oxygen on Everest is ___.
You are right on the first one.
On the second, it is 1/3 (without nitpicking about the composition of the atmosphere vs altitude).
To answer the first question, we need to consider the concept of molar volume. Molar volume is the volume occupied by one mole of a gas at a specific temperature and pressure. According to Avogadro's Law, equal volumes of gases at the same temperature and pressure contain an equal number of molecules.
In this case, we have 0.20 mol of carbon dioxide occupying a volume of 3.1 L. Therefore, the molar volume of carbon dioxide at that temperature and pressure is 3.1 L / 0.20 mol = 15.5 L/mol.
Now, if we have a 3.1-L sample of hydrogen at the same temperature and pressure, we can figure out the number of moles of hydrogen by dividing the sample volume by the molar volume: 3.1 L / 15.5 L/mol = 0.20 mol.
Hence, the 3.1-L sample of hydrogen at the same temperature and pressure contains the same number of moles (and therefore the same number of molecules) as the 0.20 mol of carbon dioxide.
For the second question, we need to understand Dalton's Law of Partial Pressures. According to this law, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each gas.
If the atmospheric pressure on Mt. Everest is one-third the atmospheric pressure at sea level, we can say that the partial pressure of oxygen on Everest is also one-third of the partial pressure at sea level.
So if the partial pressure of oxygen at sea level is X, then the partial pressure of oxygen on Everest would be (1/3) * X.
Therefore, the partial pressure of oxygen on Everest is one-third of the partial pressure at sea level.