Step 1: State Graham's law of diffusion: The rate of diffusion of a gas is inversely proportional to the square root of its molar mass. The relationship is expressed as \[ \text{Rate} \propto \frac{1}{\sqrt{M}}, \] where \( M \) represents the molar mass of the gas.
Step 2: List the molar masses of the gases provided:
- O\(_2\): \( 32 \, \text{g/mol} \),
- CO\(_2\): \( 44 \, \text{g/mol} \),
- H\(_2\): \( 2 \, \text{g/mol} \),
- N\(_2\): \( 28 \, \text{g/mol} \).
Step 3: Identify the gas with the lowest molar mass.
H\(_2\) has the lowest molar mass (2 g/mol), indicating it will diffuse at the highest rate.