The average molecular weight of a gas mixture can vary significantly when calculated using different methods
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For example: given the masses m1 and m2 of the two gases, as well as their molecular weights M1 and M2, it is possible to calculate their respective amounts n1 and n2, as well as their volume fractions V1 and V2. There are two methods for determining the average molecular weight of the mixed gas: 1. (m1+m2)/(n1+n2) 2. M1*V1+M2*V2. Sometimes, these two methods yield different results; in some cases, the result obtained using the first method is higher than the molecular weights of each individual gas. What is the reason for this?
Use the first method, but the second algorithm is the same as the first, because the volume fraction is also converted based on molar amounts. The discrepancy you mentioned might be caused by omitting the decimal point in the step-by-step calculations. Additionally, as for the situation you mentioned where the value is greater than both molecular weights, I haven’t encountered it; unless you made a calculation mistake. Take an example and have a look.
These two algorithms are consistent; by replacing m in the first formula with M*n and substituting it into the formula, the second formula can be derived. Therefore, there is no inconsistency as you mentioned.
Calculations related to the average molecular weight of a gas mixture (1) Basis for calculation: ① The mass of 1 mol of any substance is numerically equal to its molar mass. ② The volume of 1 mol of any gas is numerically equal to the molar volume of that gas (expressed in L·mol-1). (2) Basic calculation relationship: M(-) (3) Derived calculation relationships: ① M(-) = ② M(-) = The formulas in ① and ② are applicable to the calculation of all mixtures. ② The formula in ③ is only applicable to calculations related to gas mixtures. ③ Avogadro’s law is applied between the two formulas in ③