Question

calculate the volume of one mole of oxygen at 27degree centigrade and 4atm pressure. The molar volume of oxygen at NTP is 22.4 litres.

Answer 1

calculate the volume of one mole of oxygen at 27degree centigrade and 4atm pressure. The molar volume of oxygen at NTP is 22.4 litres.

Solution

NTP - Normal Temperature and Pressure - is defined as air at $20^{\circ}C$ (293.15 K, $68^{\circ}F$) and 1 atm (101.325 kN/m², 101.325 kPa, 14.7 psia, 0 psig, 29.92 in Hg, 760 torr).

One can use the combined gas law:

$$\frac{pV}{T} = \text{const}$$ $$\frac{p_1 V_1}{T_1} = \frac{p_2 V_2}{T_2}$$

As we have 1 mol of gas we can rewrite the last formulae

$$\frac{p_1 V_1^m}{T_1} = \frac{p_2 V_2^m}{T_2}$$

Where $V^m$ is a molar volume.

$$\frac{1 \text{atm} \cdot 22.4 L}{293 K} = \frac{4 \text{atm} \cdot V_2^m}{(27 + 273) K}$$ $$V_2^m = \frac{1 \text{atm} \cdot 22.4 L \cdot (27 + 273) K}{293 K \cdot 4 \text{atm}} = 5.7 L$$

Answer: $V^m(300K, 4\text{atm}) = 5.7L$