Final answer:
The final pressure of SO2 gas after being heated from 0.0°C to 343°C and compressed is 33.00 atm. To determine the final volume, we calculate moles from the given mass and use the ideal gas law to find the final volume at the final pressure and temperature.
Step-by-step explanation:
To determine the final pressure of SO2 gas after heating and compression, we can use the combined gas law, which is P1V1/T1 = P2V2/T2. First, convert all temperatures to Kelvins by adding 273.15, so 0.0°C becomes 273.15 K and 343°C becomes 616.15 K. Given initial conditions: P1 = 6.60 atm, V1 = V (unknown), T1 = 273.15 K, and the final conditions: V2 = V1/5, T2 = 616.15 K. We solve for P2 using the ratio of initial to final pressures and volumes.
The formula rearranges to P2 = P1V1T2 / (V2T1). Plugging in the values, we get P2 = (6.60 atm × 1 × 616.15 K) / (1/5 × 273.15 K). Simplifying, P2 = 33.00 atm.
To find the final volume, we must first determine the amount of gas using the ideal gas law PV=nRT. We know P, we know n can be calculated from the mass and molar mass of SO2, R is the ideal gas constant of 0.0821 L atm K⁻¹ mol⁻¹, and T is the final temperature. V = nRT/P, so after determining n, we can solve for V.2.
Mass of SO2 = 14.6 g, Molar mass of SO2 = 64.07 g/mol, therefore n = 14.6 g / 64.07 g/mol. We can then find the volume V2 using V = nRT/P after calculating the number of moles.