Question

A 2.8 L sample of carbon dioxide gas is at STP. The gas is transferred to a vessel and the volume is adjusted to 0.45 L and the temperature is brought to 340°C. What is the pressure, in mmHg, of the gas sample under these new conditions

Answer 1

Under the new conditions of 0.45 L and 340°C, the pressure of the carbon dioxide gas sample is approximately 9350.192 mmHg. This can be calculated using the combined gas law equation and converting the result from atm to mmHg.

Step-by-step explanation:

Under the new conditions of 0.45 L and 340°C, we can use the combined gas law to calculate the pressure of the gas sample. The combined gas law states that, for a given amount of gas, the product of the initial pressure and volume divided by the initial temperature is equal to the product of the final pressure and volume divided by the final temperature.

Using the given values:

• Initial pressure (P1) = 1 atm
• Initial volume (V1) = 2.8 L
• Initial temperature (T1) = 0°C (273 K)
• Final volume (V2) = 0.45 L
• Final temperature (T2) = 340°C (613 K)

Plugging in the values to the combined gas law equation, we have:

P1 * V1 / T1 = P2 * V2 / T2

Solving for P2 (the final pressure), we get:

P2 = (P1 * V1 * T2) / (V2 * T1)

Substituting the values, we get:

P2 = (1 atm * 2.8 L * 613 K) / (0.45 L * 273 K)

P2 ≈ 12.292 atm

Since the pressure is often expressed in mmHg, we can convert 12.292 atm to mmHg by multiplying it by 760 mmHg/atm:

P2 ≈ 9350.192 mmHg

Therefore, the pressure of the carbon dioxide gas sample under the new conditions is approximately 9350.192 mmHg.