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If two gases have molar masses M1, and M2 Graham’s law
Chapter 3, Problem 10SE(choose chapter or problem)
If two gases have molar masses \(M_{1}\) and \(M_{2}\), Graham's law states that the ratio of their rates of effusion through a small opening is given by \(R=\sqrt{M_{1} / M_{2}}\). The effusion rate of an unknown gas through a small opening is measured to be \(1.66 \pm 0.03\) times greater than the effusion rate of carbon dioxide. The molar mass of carbon dioxide may be taken to be 44 g/mol with negligible uncertainty.
a. Estimate the molar mass of the unknown gas, and find the uncertainty in the estimate.
b. Find the relative uncertainty in the estimated molar mass.
Equation Transcription:
Text Transcription:
M_1
M_2
R=sqrt{M_1/M_2}
1.66{+/-}0.03
Questions & Answers
QUESTION:
If two gases have molar masses \(M_{1}\) and \(M_{2}\), Graham's law states that the ratio of their rates of effusion through a small opening is given by \(R=\sqrt{M_{1} / M_{2}}\). The effusion rate of an unknown gas through a small opening is measured to be \(1.66 \pm 0.03\) times greater than the effusion rate of carbon dioxide. The molar mass of carbon dioxide may be taken to be 44 g/mol with negligible uncertainty.
a. Estimate the molar mass of the unknown gas, and find the uncertainty in the estimate.
b. Find the relative uncertainty in the estimated molar mass.
Equation Transcription:
Text Transcription:
M_1
M_2
R=sqrt{M_1/M_2}
1.66{+/-}0.03
ANSWER:
Solution 10SE
Step1 of 3:
Let us consider be the molar mass of unknown gas and
be the molar mass of carbon dioxide.
We have Graham’s law and it states that the ratio R of their rates of effusion through a small opening is given by
R =
And also we have the effusion rate of an unknown gas through a small opening is Measured to be 1.66 ± 0.03 times greater than the effusion rate of carbon dioxide.
That is effusion rate of carbon dioxide is R = 1.66,g/mol.
Here our goal is:
a).We need to estimate the molar mass of the unknown gas, and find the uncertainty in the estimate.
b).We need to find the relative uncertainty in the estimated molar mass.
Step2 of 3:
a).
Let us consider the equation: