Answer and Explanation:
To find the relative density of the gas, we need to use the ratio of the rates of diffusion. The ratio given is 300:200, which represents the rate of diffusion of the gas to the rate of diffusion of CO2.
The rate of diffusion is inversely proportional to the square root of the relative molecular mass. Therefore, we can set up the following equation:
Rate of diffusion of gas / Rate of diffusion of CO2 = √(Relative molecular mass of CO2 / Relative molecular mass of the gas)
Since the rate of diffusion of CO2 is in the denominator, we can write the equation as:
Rate of diffusion of gas / Rate of diffusion of CO2 = √(Relative molecular mass of CO2 / Relative molecular mass of the gas) = 300 / 200
To find the relative density, we can square both sides of the equation:
(√(Relative molecular mass of CO2 / Relative molecular mass of the gas))^2 = (300 / 200)^2
Simplifying this equation, we get:
Relative molecular mass of CO2 / Relative molecular mass of the gas = (300 / 200)^2 = 9 / 4
Cross-multiplying the equation, we have:
Relative molecular mass of CO2 = (9 / 4) * Relative molecular mass of the gas
Since relative density is defined as the ratio of the mass of a substance to the mass of an equal volume of a reference substance (usually water), we can substitute relative molecular mass with relative density in this equation:
Relative density of CO2 = (9 / 4) * Relative density of the gas
Therefore, the relative density of the gas is 9/4 times the relative density of CO2.