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Question 8

The volume $$V$$ of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature $$T$$. Consider $$R$$ as universal gas constant. The pressure of the mixture of gases is:

We need to find the total pressure of a mixture of gases in a volume $$V$$ at temperature $$T$$. First, we calculate the number of moles of each gas.

For oxygen ($$O_2$$, molar mass 32 g/mol): $$n_{O_2} = \frac{16}{32} = 0.5$$ mol.

For nitrogen ($$N_2$$, molar mass 28 g/mol): $$n_{N_2} = \frac{28}{28} = 1$$ mol.

For carbon dioxide ($$CO_2$$, molar mass 44 g/mol): $$n_{CO_2} = \frac{44}{44} = 1$$ mol.

The total number of moles is $$n = 0.5 + 1 + 1 = 2.5 = \frac{5}{2}$$ mol.

By Dalton's law of partial pressures (or equivalently, the ideal gas law for the mixture), the total pressure is $$P = \frac{nRT}{V} = \frac{5}{2} \cdot \frac{RT}{V}$$.

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