A sample of gas at 35degree Celsius and 1 atm occupies a volume of 37.5L. At what temp should the gas be kept, if it required to reduce the volume to 3.0 litre at the same pressure?

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Answer 1 · 2017-06-07T18:27:29

The gas should be kept at -248 degrees C.

Use Charles Law. Temperature and Volume are directly related using degrees Kelvin. ( if the pressure and number of molecules are kept constant.

$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$ $V_1/T_1 = V_2/T_2$

$V_{1} = 37.5 l$ $V_1 = 37.5l$
$T_{1} = 35 + 273 = 308$ $T_1 = 35 + 273 = 308$ degrees K
$V_{2} = 3.0 l$ $V_2 = 3.0l$
# T_2 = unknown

Substituting these numbers into the equation gives

$\frac{37.5}{308} = \frac{3.0}{T_{2}}$ $37.5/308 = 3.0/ T_2$ multiplying across gives

$T_{2} = 308 \times \frac{3.0}{37.5}$ $T_2 = 308 xx 3.0/37.5$ Which gives

# T_2 = 24.6 degrees K

Subtract 273 to find degrees C.

$24.6 - 273 = - 248$ $24.6 -273 = -248$ degrees C. ( to three significant digits.)