it takes a certain gas 1.98 times as long to diffuse as an equal volume of helium under the same conditions. what is the calculated molecular weight of the gas?
Isn't this Graham's law of diffusion
rate1/rate2 = sqrt(mass2)/sqrt(mass1)
1.98= sqrt (mass1/4)
square both sides, multiply both sides by 4.
In my head, it is about 16
Core of Graham's law of diffusion
r¹/r²=√(M²/M¹ )
2.3=√(M¹/32)
Sq. both sides & multiply both side by 32
My head dictates it 169
To calculate the molecular weight of the gas, we'll first need to understand the concept of diffusion and how it relates to the molecular weight of gases.
Diffusion is the process by which molecules move from an area of high concentration to an area of low concentration. The rate at which a gas diffuses is influenced by its molecular weight. A lighter gas will diffuse faster than a heavier gas under the same conditions because the lighter molecules have higher average speeds.
Given that it takes the gas 1.98 times as long to diffuse compared to an equal volume of helium, we can use this information to determine the molecular weight ratio between the two gases.
First, let's assign some variables:
- t_gas: Time taken for the gas to diffuse
- t_helium: Time taken for an equal volume of helium to diffuse
According to the given information, the gas takes 1.98 times longer to diffuse compared to helium, so we have the equation:
t_gas = 1.98 * t_helium
Now, let's consider Graham's Law of Diffusion, which states that the ratio of the diffusion rates of two gases is inversely proportional to the square root of their molecular weights. Mathematically, this can be expressed as:
Rate_gas / Rate_helium = √(M_helium / M_gas)
We can rewrite this equation as:
t_helium / t_gas = √(M_helium / M_gas)
Substituting the equation from the given information:
t_helium / (1.98 * t_helium) = √(M_helium / M_gas)
Simplifying, we get:
1 / 1.98 = √(M_helium / M_gas)
Squaring both sides, we have:
1 / 3.92 = M_helium / M_gas
Solving for M_gas, the molecular weight of the gas, we get:
M_gas = M_helium * 3.92
So, to calculate the molecular weight of the gas, you will need to know the molecular weight of helium and multiply it by 3.92.