A syringe contains 589 mL of CO at 325 K and 1.2 bar. A second syringe contains 473 mL of N₂ at 298 K and 2.6 bar. What is the final pressure if the contents of these two syringes are injected into a 1.00 L container at 273 K? A) 0.59 bar B) 1.1 bar C) 1.7 bar D) 1.9 bar E) 3.8 bar

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Quizplus · Accepted Answer

First, we need to calculate the number of moles of CO and N₂ using the ideal gas law: $n = \frac{PV}{RT}$ For CO: $n_{CO} = \frac{(1.2\ bar)(0.589\ L)}{(0.0831\ L\cdot bar/mol\cdot K)(325\ K)} = 0.028\ mol$ For N₂: $n_{N₂} = \frac{(2.6\ bar)(0.473\ L)}{(0.0831\ L\cdot bar/mol\cdot K)(298\ K)} = 0.058\ mol$ Next, we need to calculate the total number of moles and the total volume of the gases when they are mixed together: $n_{total} = n_{CO} + n_{N₂} = 0.028\ mol + 0.058\ mol = 0.086\ mol$ $V_{total} = 0.589\ L + 0.473\ L + 1.00\ L = 2.062\ L$ Then, we can use the ideal gas law again to calculate the final pressure: $P_{final} = \frac{n_{total}RT}{V_{total}} = \frac{(0.086\ mol)(0.0831\ L\cdot bar/mol\cdot K)(273\ K)}{2.062\ L} = 1.7\ bar$ Therefore, the final pressure is 1.7 bar, which is choice C.

A Syringe Contains 589 ML of CO at 325 K