Final answer:
Using Charles's Law, the volume of the gas at -15.8°C and a constant pressure would be approximately 11.60 L after converting the temperatures to Kelvin and applying the formula V2 = (V1 × T2) / T1.
Step-by-step explanation:
The student's question relates to the application of the combined gas law to determine the volume of a gas under different conditions of temperature and pressure. Here, the student wants to know the volume of a gas sample when the temperature decreases from 65.5°C to -15.8°C while the pressure remains constant at 524 mmHg.
To answer this question, we apply the combined gas law, which combines Charles's Law, Boyle's Law, and Gay-Lussac's Law. The equation is (P1V1/T1) = (P2V2/T2), where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures in Kelvin. In this case, since the pressure does not change, the direct relationship between temperature and volume by Charles's Law can be used: (V1/T1) = (V2/T2).
First, convert the temperatures from Celsius to Kelvin by adding 273.15 to each temperature. Then, solve for the unknown volume, V2, using the initial volume V1, initial temperature T1, and final temperature T2.
Conversion to Kelvin and Calculation
Initial temperature (T1) = 65.5°C = 65.5 + 273.15 = 338.65 K
Final temperature (T2) = -15.8°C = -15.8 + 273.15 = 257.35 K
Initial volume (V1) = 15.31 L
The pressure remains constant.
Applying Charles's Law, we get:
V2 = (V1 × T2) / T1
V2 = (15.31 L × 257.35 K) / 338.65 K
V2 = 11.60 L (rounded to two decimal places)
Therefore, the final volume of the gas at -15.8°C and a pressure of 524 mmHg would be approximately 11.60 L.