True or False?
An identical cylinder filled with the same pressure of hydrogen contains more molecules because hydrogen molecules are smaller than oxygen molecules.
To determine the answer to the question, we need to compare the number of molecules in a cylinder filled with hydrogen to the number of molecules in a cylinder filled with oxygen.
To start, we need to understand the concept of the Ideal Gas Law, which states that the number of molecules (or particles) in a gas is directly proportional to its pressure, volume, and temperature. The formula for the Ideal Gas Law is:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles
R is the ideal gas constant
T is the temperature in Kelvin
In this case, the pressure and volume of the cylinders are assumed to be the same, so we can compare the number of moles of hydrogen and oxygen.
Now, let's consider the molecular mass of each gas. The molar mass of hydrogen (H2) is approximately 2 grams per mole, and the molar mass of oxygen (O2) is approximately 32 grams per mole.
Since the pressure and volume are the same, we can use the formula: PV = nRT.
If we rearrange the formula to solve for the number of moles (n), we get: n = PV / RT.
Since the pressure, volume, and gas constant (R) are all the same, we can compare the number of moles by dividing the mass of the gas by its molar mass.
For hydrogen: n(H2) = mass(H2) / molar mass(H2) = mass(H2) / 2 g/mol.
For oxygen: n(O2) = mass(O2) / molar mass(O2) = mass(O2) / 32 g/mol.
Given the same pressure and volume, the number of moles depends only on the mass of the gas and its molar mass.
Therefore, to answer the original question, we need to compare the masses of hydrogen and oxygen in the identical cylinders. If the mass of hydrogen in the cylinder is greater than the mass of oxygen, then it is true that the cylinder filled with hydrogen will contain more molecules. Otherwise, if the mass of oxygen is greater, then it is false.
However, the question does not provide information about the masses of the gases, so it is not possible to determine whether the statement is true or false based solely on the given information.