Question

During laparoscopic surgery, carbon dioxide gas is used to expand the abdomen to help create a larger working space.

If 4.40 L of CO₂ gas at 13∘C at 795 mmHg is used, what is the final volume, in liters, of the gas at 35 ∘C and a pressure of 741 mmHg , if the amount of CO₂ remains the same?

Answer 1

The final volume of CO₂ gas at 35 °C and 741 mmHg can be calculated using the combined gas law formula V2 = P1V1T2/(P2T1), after converting temperatures to Kelvin.

Step-by-step explanation:

To calculate the final volume of CO₂ at 35 °C and 741 mmHg, we can use the combined gas law which relates pressure, volume, and temperature of a gas. The combined gas law is: P1V1/T1 = P2V2/T2, where P1 and V1 are the initial pressure and volume, T1 is the initial temperature, P2 and V2 are the final pressure and volume, and T2 is the final temperature.

We first need to convert all temperatures to Kelvin by adding 273.15. Therefore, T1 is 13 °C + 273.15 = 286.15 K and T2 is 35 °C + 273.15 = 308.15 K.

Next, we rearrange the combined gas law to solve for V2: V2 = P1V1T2/(P2T1). Substituting the given values:

• P1 = 795 mmHg
• V1 = 4.40 L
• T1 = 286.15 K
• P2 = 741 mmHg
• T2 = 308.15 K

Plugging into the formula, we get:

V2 = (795 mmHg) * (4.40 L) * (308.15 K) / (741 mmHg) * (286.15 K)

After performing the calculations, we find the final volume V2. It's important to note that when making these calculations, the unit for pressure (mmHg) remains consistent, so it does not need to be converted.