The molar mass (M) of an ideal gas may be calculated from the ideal gas law PV =

Question

The molar mass (M) of an ideal gas may be calculated from the ideal gas law PV = WRT/M In an experiment with C_3H_s(g), a student obtained the following values and associated errors or standard deviations: p = 745 plusminus 2 mmHg V = 200 plusminus 2 ml W = 351 plusminus 4 mg T = 25 plusminus 1 degree C R = 0.082106 L atm middot K^-1 mol^-1 (neglect the uncertainty of R) Calculate the molar mass from the ideal gas equation, the percent difference from the "true" molar mass, and its standard deviation. (Ignore the covariance.) What would be the standard deviation of the molar mass if the uncertainty in R is plusminus 0.00005?

Explanation / Answer

From ideal gas equation

PV = nRT

PV = WRT/M

M = WRT / PV

= (0.351 * 0.082 * 298 * 760 ) / (745 * 0.2)

M = 43.74 g/mol

True Molar mass = 44 g/ mol

Percentage difference = (44 - 43.74) * 100 /44 = 0.57 %

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