A biogas mixture from a landfill contains 16.0 g of methane ( , molar mass = 16.0 g/mol), 28.0 g of carbon monoxide ( , molar mass = 28.0 g/mol), and 44.0 g of carbon dioxide ( , molar mass = 44.0 g/mol). The total pressure of the mixture is 270 kPa. Calculate the partial pressure of in the biogas.
Answer & Analysis
Analysis
Question Analysis
This question involves converting the mass of three distinct biogas components to moles, calculating total moles of the mixture, and applying the mole fraction form of Dalton’s Law of Partial Pressures. The main focus is on integrating stoichiometric mass-mole conversion with partial pressure calculation for an environmentally relevant gas mixture.
Key Concept Explanation
For mass-based multi-component gas mixtures, the core relationships are:
1. Moles calculation: (where = mass, = molar mass).
2. Mole fraction: (sum of all mole fractions = 1).
3. Partial pressure: .
This method is valid only for non-reacting ideal gas mixtures (biogas components do not react under standard conditions).
Step-by-Step Solution
1. Calculate moles of each gas:
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