A certain volume of oxygen diffused from a given apparatus in 125 seconds. In the same conditions , the same volume of gas N, diffused in 100 seconds . Calculate the relative molecular mass of N(=16.0).
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rate oxygen = V/125 s
rate N gas = V/100 s
molar mass O2 = 32
molar mass N = ?
mm stands for molar mass
(rate 1)/(rate 2) = sqrt (mm N/mm O2)
(V/125)/(V/100) = sqrt (mm N/32)
Solve for molar mass N.
Post your work if you get stuck.
To calculate the relative molecular mass of gas N, 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.
Let's denote the rate of diffusion of oxygen as rO2 and the rate of diffusion of gas N as rN.
According to the given information, the volume of oxygen diffused in 125 seconds is equal to the volume of gas N diffused in 100 seconds. Therefore, we can write the following equation:
Volume of oxygen / Time taken for oxygen = Volume of gas N / Time taken for gas N
Since the volume of gas is the same, we can express the equation as:
rO2 / 125 = rN / 100
To find the relative molecular mass of gas N, we need to find the ratio of the rates of diffusion, which we will denote as MR (molar ratio). This can be written as:
MR = (rate of diffusion of oxygen) / (rate of diffusion of gas N)
= rO2 / rN
To calculate MR, we can rearrange the earlier equation:
MR = (rO2 / 125) * (100 / rN)
= (100 / 125) * (rO2 / rN)
Substituting the known molar mass of oxygen (32.0) and the given molar mass of gas N (16.0), we can create another equation:
MR = (100 / 125) * (rO2 / rN) = √(molar mass of gas N / molar mass of oxygen) = √(16.0 / 32.0) = √0.5
Therefore, the relative molecular mass of gas N is equal to the square of this ratio:
Relative molecular mass of gas N = (MR)^2 = (√0.5)^2 = 0.5
Hence, the relative molecular mass of gas N is 0.5.