A sample of gas in a closed container at a temperature of 100oC and 3 atm is heated to 300oC. What is the pressure of the gas at the higher temperature?

6.14 atm

Explanation:

Initial temperature (T₁) = 100 °C

Initial pressure (P₁) = 4 atm

Final temperature (T₂) = 300 °C

Final pressure (P₂) =?

NOTE: Volume = constant (since the system is a closed system)

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

T(K) = T(°C) + 273

Initial temperature (T₁) = 100 °C

Initial temperature (T₁) = 100 °C + 273 = 373 K

Final temperature (T₂) = 300 °C

Final temperature (T₂) = 300 °C + 273 = 573 K

Finally, we shall determine the pressure at the highest temperature as follow:

Initial temperature (T₁) = 373 K

Initial pressure (P₁) = 4 atm

Final temperature (T₂) = 573 K

Final pressure (P₂) =?

P₁ / T₁ = P₂ / T₂

4 / 373 = P₂ / 573

Cross multiply

373 × P₂ = 4 × 573

373 × P₂ = 2292

Divide both side by 373

P₂ = 2292 / 373

P₂ = 6.14 atm

Thus, the pressure at the highest temperature is 6.14 atm

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