Question

During laparoscopic surgery , carbon dioxide gas is used to expand the abdomen to help create a larger working space. If 4.80 L of CO₂ gas at 18 °C at 785 mmHg is used, what is the final volume , in liters, of the gas at 37 degrees * C and a pressure of 745 mmHg if the amount of CO₂ does not change ? (8.5)

Answer 1

The final volume of CO₂ at 37 °C and 745 mmHg, when starting with a volume of 4.80 L at 18 °C and 785 mmHg, is found using the combined gas law and is calculated to be 5.09 liters.

Step-by-step explanation:

The question involves using the ideal gas law to find the final volume of carbon dioxide (CO₂) gas under new conditions of temperature and pressure during laparoscopic surgery. Initially, the gas has a volume of 4.80 L, a temperature of 18 °C, and a pressure of 785 mmHg. We are asked to find the final volume at a temperature of 37 °C and a pressure of 745 mmHg, assuming the amount of CO₂ remains constant. To solve this, we can use the combined gas law which is given by:

V1/T1 * P1 = V2/T2 * P2, where V is volume, T is temperature in Kelvin, and P is pressure. Using this equation, the final volume (V2) can be calculated as follows:
V2 = (V1 * P1 * T2) / (T1 * P2)

Before we can use this formula, temperatures must be converted from Celsius to Kelvin by adding 273.15. Thus, we get:
T1 = 18 °C + 273.15 K = 291.15 K
T2 = 37 °C + 273.15 K = 310.15 K

Now, substituting the given values into the formula:

V2 = (4.80 L * 785 mmHg * 310.15 K) / (291.15 K * 745 mmHg)
V2 = 5.09 L (after calculation)

Hence, the final volume of CO₂ at 37 °C and 745 mmHg is 5.09 liters.