A gas occupies 3 litres at 0°C. what volume will it occupy at -20°C, assuming pressure remaining constant?

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A gas occupies 3 litres at 0°C. what volume will it occupy at -20°C, assuming pressure remaining constant?

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Answer 1 · 2017-11-22T14:28:15

2.78 litres

Explanation:

If you treat it as an ideal gas, then $P V = n R T$ $PV=nRT$ where P is pressure, V is volume, n is number of moles, R is the gas constant and T is temperature in K.

If you assume pressure is constant, and we know that the amount of substance will remain constant, and of course the gas constant is a constant, then $V$ $V$ varies directly with $T$ $T$ . So for the two temperatures you can say:

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

$T_{2}$ $T_2$ , the higher of the two temperatures, will be 273 K and $T_{1}$ $T_1$ will be 20 degrees lower, so 253 K.

Now plug in the numbers:

$V_{2} = \frac{3.253}{273} = 2.78$ $V_2 = (3 . 253)/(273) = 2.78$ litres.

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A gas occupies 3 litres at 0°C. what volume will it occupy at -20°C, assuming pressure remaining constant?

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