Question

One mole of a gas occupies 22.4 liters at 0°C and 760 mm Hg. Calculate the pressure needed to compress 2.00 moles of oxygen into a 3.00-liter container maintained at 25°C.

Answer 1

Answer on Question #74192, Physics / Electromagnetism |

Question

One mole of a gas occupies 22.4 liters at 0°C and 760 mm Hg. Calculate the pressure needed to compress 2.00 moles of oxygen into a 3.00-liter container maintained at 25°C.

Solution

$v_{1} = 1mol$ $v_{2} = 1mol$

$V_{1} = 22.4l$ $V_{2} = 3l$

$T_{1} = 273K$ $T_{2} = 298K$

$P_{1} = 760mmHg$ $P_{2} - ?$

From ideal gas law we have

$P_{1}V_{1} = v_{1}RT_{1},$

$P_{2}V_{2} = v_{2}RT_{2},$

which gives

$P_{2} = P_{1}\frac{v_{2}T_{2}V_{1}}{v_{1}T_{1}V_{2}} = 760mmHg\frac{2mol\cdot 298K\cdot 22.4l}{1mol\cdot 273K\cdot 3l} = 12388.6mmHg.$

Answer: $P_{2} = 12388.6mmHg$.

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