A certain volume of co2 take 200 sec to diffuse through a porous plug how long eill it take the same volumeof hydrogen chloride gas to diffuse under same condition
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To determine the time it takes for the same volume of hydrogen chloride (HCl) gas to diffuse through a porous plug under the same conditions, we need to apply Graham's Law of diffusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
1. Find the molar masses of both CO2 and HCl:
- Molar mass of CO2 (carbondioxide) = 12.01 g/mol (molar mass of carbon) + (2 × 16.00 g/mol) (molar mass of oxygen) = 44.01 g/mol
- Molar mass of HCl (hydrogen chloride) = 1.01 g/mol (molar mass of hydrogen) + 35.45 g/mol (molar mass of chlorine) = 36.46 g/mol
2. Calculate the square root of the molar masses:
- √Molar mass of CO2 = √44.01 g/mol ≈ 6.63 g/mol
- √Molar mass of HCl = √36.46 g/mol ≈ 6.04 g/mol
3. Apply Graham's Law of diffusion to find the ratio of the diffusion rates:
- Rate of diffusion of CO2 / Rate of diffusion of HCl = √Molar mass of HCl / √Molar mass of CO2
- Rate of diffusion of CO2 / Rate of diffusion of HCl = 6.04 g/mol / 6.63 g/mol ≈ 0.912
4. Since the rates of diffusion are inversely proportional to the square roots of the molar masses, the ratio calculated above represents the time it takes for HCl to diffuse compared to CO2 in the same conditions.
5. Therefore, it will take approximately 0.912 times the time it took for CO2 to diffuse through the porous plug for the same volume of HCl to diffuse under the same conditions.
6. If it took 200 seconds for CO2 to diffuse through the porous plug, the time it would take for the same volume of HCl to diffuse would be:
- Time for HCl = 0.912 × 200 seconds = 182.4 seconds
Thus, it will take approximately 182.4 seconds for the same volume of hydrogen chloride gas to diffuse through the porous plug under the same conditions.