Which of the following gases effuses the fastest at a given temperature?
Ne
CH4
Ar
H2
H2
The rate of effusion depends on the molar mass of the gas. Lighter gases effuse faster compared to heavier gases at a given temperature.
Among the given options, the gas that effuses the fastest is hydrogen (H2). It has the lowest molar mass of all the options and therefore will effuse the fastest.
To determine which gas will effuse the fastest at a given temperature, we can use Graham's Law of Effusion. According to Graham's Law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
Here's how you can calculate which gas effuses the fastest from the provided options:
Step 1: Find the molar mass for each gas.
- Ne (Neon) has a molar mass of approximately 20.18 g/mol.
- CH4 (Methane) has a molar mass of approximately 16.04 g/mol.
- Ar (Argon) has a molar mass of approximately 39.95 g/mol.
- H2 (Hydrogen) has a molar mass of approximately 2.02 g/mol.
Step 2: Calculate the square root of each gas's molar mass.
- The square root of Ne's molar mass is √20.18 ≈ 4.49 g/mol.
- The square root of CH4's molar mass is √16.04 ≈ 4.00 g/mol.
- The square root of Ar's molar mass is √39.95 ≈ 6.32 g/mol.
- The square root of H2's molar mass is √2.02 ≈ 1.42 g/mol.
Step 3: Compare the square roots of the molar masses.
- The gas with the smallest square root of molar mass will effuse the fastest. In this case, H2 has the smallest square root value of 1.42 g/mol.
Therefore, based on Graham's Law, H2 (Hydrogen) will effuse the fastest at a given temperature among the provided options.