Question

A sample of carbon dioxide gas occupies 638 mL at 0.893 atm and 12°C. What will the pressure be at a volume of 881 mL and a temperature of 18°C?

Short answer

The final pressure will be approximately 0.740 atm.

Step-by-step solution

Write down the given information

Initial volume (V_1) = 638 mL, initial pressure (P_1) = 0.893 atm, initial temperature (T_1) = 12°C. Final volume (V_2) = 881 mL, final temperature (T_2) = 18°C.

Convert temperatures to Kelvin

Convert the temperatures from Celsius to Kelvin by adding 273.15. T_1 = 12 + 273.15 = 285.15 K. T_2 = 18 + 273.15 = 291.15 K.

Use the Combined Gas Law

The Combined Gas Law is given by: \[\frac{P_1 \times V_1}{T_1} = \frac{P_2 \times V_2}{T_2}\]. Rearrange it to solve for P_2: \[P_2 = \frac{P_1 \times V_1 \times T_2}{T_1 \times V_2}\].

Substitute the known values

Substitute the known values into the equation: \[P_2 = \frac{0.893 \times 638 \times 291.15}{285.15 \times 881}\].

Calculate the final pressure

Perform the calculation: \[P_2 \approx \frac{0.893 \times 638 \times 291.15}{285.15 \times 881} \approx 0.740 \text{ atm}\].

Key concepts

Joules Thompson effect

The Joules Thompson effect is an important concept in thermodynamics, particularly when dealing with gases. It describes the temperature change of a gas when it is forced through a valve or porous plug while kept insulated so that no heat is exchanged with the environment. This phenomenon, also known as Joule-Thomson expansion, helps understand why certain gases cool upon expansion and others may heat up. It is critical in industrial applications like refrigeration and liquefaction of gases. When a gas undergoes this process, its internal energy changes because of work done by pressure differences. In simpler words, the gas either absorbs or releases heat, leading to a change in temperature. Always consider how an ideal gas might behave differently from real gases under such conditions.

pressure calculation

Pressure calculation is fundamental in understanding how gases behave under various conditions. The original exercise requires calculating the final pressure of a gas sample when its volume and temperature change using the Combined Gas Law.

The Combined Gas Law integrates Boyle's Law, Charles' Law, and Gay-Lussac's Law into one equation:

gas laws

Gas laws are crucial for predicting how gases will react under different conditions of temperature, volume, and pressure. In our exercise, the Combined Gas Law is used, but there are other specific gas laws that contribute to it

• Boyle's Law states that pressure is inversely proportional to volume when temperature remains constant ewline
• Charles's Law says that volume is directly proportional to temperature when pressure is constant
• Gay-Lussac's Law explains that pressure is directly proportional to temperature when volume is constant
  
  Understanding these individual laws helps to grasp the behavior of gases more completely. Using the Combined Gas Law brings together these principles to resolve more complex scenarios where multiple parameters change simultaneously.