If 30cm3 of oxygen diffuses through a porous plug in 7secs how long will it take 60cm3 of chlorine to diffuses through the same plug,( O-16, C-55.5 )
We cannot use the molecular weights of oxygen and chlorine to solve this problem, as diffusion rates are not directly proportional to molecular weights. Instead, we can use Graham's law of effusion, which states that the rate of effusion (or diffusion) of a gas is inversely proportional to the square root of its molecular weight.
Let's denote the time it takes for chlorine to diffuse through the same plug as t. Then, we can set up the following equation using Graham's law:
(rate of oxygen diffusion) / (rate of chlorine diffusion) = sqrt(molecular weight of chlorine / molecular weight of oxygen)
We know that the rate of oxygen diffusion is 30 cm^3 / 7 sec, and we want to solve for t when the rate of chlorine diffusion is 60 cm^3 / t sec. The molecular weights of oxygen and chlorine can be looked up as approximately 32 g/mol and 71 g/mol, respectively. Substituting these values and solving for t, we get:
(30 cm^3 / 7 sec) / (60 cm^3 / t sec) = sqrt(71 g/mol / 32 g/mol)
t = (7 sec) * (sqrt(32 g/mol / 71 g/mol)) * (60 cm^3 / 30 cm^3)
t ≈ 13 sec
Therefore, it will take approximately 13 seconds for 60 cm^3 of chlorine to diffuse through the same porous plug.
To determine how long it will take for 60 cm3 of chlorine to diffuse through the same porous plug as the oxygen, we can use Graham's Law of diffusion. Graham's law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
First, we need to calculate the rate of diffusion for oxygen and use it to find the time needed for chlorine to diffuse. Let's begin:
1. Calculate the molar mass of oxygen (O2):
- Oxygen atomic mass (O) = 16 g/mol
- Molar mass of oxygen (O2) = 2 * 16 g/mol = 32 g/mol
2. Calculate the rate of diffusion for oxygen:
- Rate of diffusion of oxygen = 30 cm3 / 7 sec = 4.29 cm3/sec
3. Calculate the molar mass of chlorine (Cl2):
- Chlorine atomic mass (Cl) = 35.5 g/mol
- Molar mass of chlorine (Cl2) = 2 * 35.5 g/mol = 71 g/mol
4. Use Graham's Law to calculate the time needed for chlorine to diffuse:
- Using the equation: (rate1 / rate2) = √(MolarMass2 / MolarMass1)
- (4.29 cm3/sec) / (x cm3/sec) = √(71 g/mol / 32 g/mol)
5. Solve for x to find the rate of diffusion of chlorine:
- x = (4.29 cm3/sec) * (√(32 g/mol / 71 g/mol))
- x ≈ 3.07 cm3/sec
6. Calculate the time needed for 60 cm3 of chlorine to diffuse:
- Time = Volume / Rate of diffusion
- Time = 60 cm3 / 3.07 cm3/sec
- Time ≈ 19.54 sec
Therefore, it will take approximately 19.54 seconds for 60 cm3 of chlorine to diffuse through the same porous plug.