A mass of gas occupies 20 cm3 at 5 degrees Celcius and 760 mm Hg pressure. What is its volume at 30 degrees Celcius and 800 mm Hg pressure?

20.7 cm³

Explanation:

From the question given above, the following data were obtained:

Initial volume (V1) = 20 cm³

Initial temperature (T1) = 5 °C

Initial pressure (P1) = 760 mm Hg

Final temperature (T2) = 30 °C

Final pressure (P2) = 800 mm Hg

Final volume (V2) =?

Next we shall convert celsius temperature to Kelvin temperature. This can be obtained as follow:

Temperature (K) = Temperature (°C) + 273

Initial temperature (T1) = 5 °C

Initial temperature (T1) = 5 °C + 273 = 278 K.

Final temperature (T2) = 30 °C

Final temperature (T2) = 30 °C + 273 = 303 K.

Finally, we shall determine the new volume of the gas as follow:

Initial volume (V1) = 20 cm³

Initial temperature (T1) = 278 K

Initial pressure (P1) = 760 mm Hg

Final temperature (T2) = 303 K

Final pressure (P2) = 800 mm Hg

Final volume (V2) =?

P1V1/T1 = P2V2/T2

760 × 20 /278 = 800 × V2/303

Cross multiply

278 × 800 × V2 = 760 × 20 × 303

Divide both side by 278 × 800

V2 = (760 × 20 × 303) / (278 × 800)

V2 = 20.7 cm³

Therefore, the new volume of the gas is 20.7 cm³

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