A sample of nitrous oxide has a volume of 120 L at 1.500 mm Hg and = 10°C. Calculate its pressure when its volume is compressed to 50 L and its temperature increased to
34°C

3.91 mmHg

Explanation:

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

Initial volume (V₁) = 120 L

Initial pressure (P₁) = 1.5 mmHg

Initial temperature (T₁) = 10 °C

Final volume (V₂) = 50 L

Final temperature (T₂) = 34 °C

Final pressure (P₂) =?

Next, we shall convert 10 °C and 34 °C to Kelvin temperature. This can be obtained as follow:

T(K) = T(°C) + 273

Initial temperature (T₁) = 10 °C

Initial temperature (T₁) = 10 °C + 273

Initial temperature (T₁) = 283 K

Final temperature (T₂) = 34 °C

Final temperature (T₂) = 34 °C + 273

Final temperature (T₂) = 307 K

Finally, we shall determine final pressure of the gas as follow:

Initial volume (V₁) = 120 L

Initial pressure (P₁) = 1.5 mmHg

Initial temperature (T₁) = 283 K

Final volume (V₂) = 50 L

Final temperature (T₂) = 307 K

Final pressure (P₂) =?

P₁V₁/T₁ = P₂V₂/T₂

1.5 × 120/283 = P₂ × 50 / 307

Cross multiply

P₂ × 50 × 283 = 1.5 × 120 × 307

P₂ × 14150 = 55260

Divide both side by 14150

P₂ = 55260 / 14150

P₂ = 3.91 mmHg

Thus, the new pressure of the gas is 3.91 mmHg

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