A certain volume of mass A recquired 120 seconds to diffuse out.An equal volume of oxygen recquired 85 seconds to diffuse out under the same conditions.what is the relative molecular mass?
To find the relative molecular mass, we can use Graham's law of effusion, which states that the rates of effusion (or diffusion) of two gases are inversely proportional to the square roots of their molar masses.
The formula for Graham's law is:
Rate A / Rate B = √(Molar mass B / Molar mass A)
Given that the rates of diffusion are equal in this case, we can set up the equation as follows:
√(Molar mass O2 / Molar mass A) = Rate A / Rate B = √(Mass B / Mass A)
Let's assume the mass of both gases is equal to 1 (unit mass) for simplicity. Now we can substitute the given times into the equation:
√(32 / Molar mass A) = 120 / 85
Squaring both sides of the equation to remove the square root:
32 / Molar mass A = (120 / 85)^2
Rearranging the equation:
Molar mass A = 32 / (120 / 85)^2
Calculating the value:
Molar mass A = 32 / (1.4118)^2
Molar mass A ≈ 32 / 1.9944
Molar mass A ≈ 16.049
Therefore, the relative molecular mass is approximately 16.049.
To find the relative molecular mass, we need to use Graham's Law of Diffusion. According to Graham's Law, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.
Let's denote the rate of diffusion of gas A as RA and the rate of diffusion of oxygen as RO. We can set up the following equation based on Graham's Law:
RA / RO = sqrt(Molar mass of RO) / sqrt(Molar mass of A)
From the given information, we know that the time required for gas A to diffuse out is 120 seconds, while the time required for oxygen to diffuse out is 85 seconds. Since the relation between time and rate of diffusion is inverse, we can write:
RA / RO = 85 / 120
Simplifying the equation, we get:
RA / RO = 17 / 24
Now, since we are assuming equal volumes for both gases, we can consider their rates of diffusion directly proportional to their molar masses:
RA / RO = Molar mass of RO / Molar mass of A
Substituting the given values, we have:
17 / 24 = Molar mass of RO / Molar mass of A
To find the relative molecular mass, we need the ratio of the molar masses. By rearranging the equation, we get:
Relative molecular mass = Molar mass of A / Molar mass of RO = (24 / 17) = 1.41
Therefore, the relative molecular mass is approximately 1.41.
Use Graham's Law of Effusion => SqrRt(M-A)/t-A = SqrRt(M-B)/t-B
SqrRt(O2)/t(O2) = SqrRt(M-B)/t(B)
=> M-B = 63.8 amu