Final answer:
Graham's Law of Effusion indicates that the ratio of the rate of diffusion of two gases is constant and solely dependent on their molar masses, independent of temperature, as long as it is the same for both gases. Therefore, the ratio of R₁/R₂ remains the same at 0 °C and 100 °C.
Step-by-step explanation:
To demonstrate that the ratio of the rate of diffusion of Gas 1 to the rate of diffusion of Gas 2, R₁/R₂, is the same at 0 °C and 100 °C, we can refer to Graham's Law of Effusion. This law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. The formula for the rate of effusion (or diffusion) is given by:
Rate of Effusion ≈ 1/√M, where M is the molar mass.
Since the conditions specify the same temperature and pressure for both gases, and temperature is measured on the Kelvin scale for gas law calculations, even though the Celsius temperatures are different, the Kelvin temperatures will maintain the ratio of absolute temperatures.
At 0 °C (273 K) and 100 °C (373 K), for two gases A and B, the ratio of their diffusion rates is: R₁/R₂ = √(M₂/M₁)
This ratio is based solely on the molar masses of the two gases and is independent of the temperature as long as the temperature is the same for both gases during comparison. Hence, regardless of whether we compare the rates of diffusion at 0 °C or 100 °C, the ratio R₁/R₂ remains unchanged.