Final answer:
The volume of sulfur dioxide at standard temperature and pressure (STP) is found using the combined gas law, by converting given temperatures to Kelvin, and rearranging the formula to solve for the unknown volume.
Step-by-step explanation:
The task is to determine the volume that sulfur dioxide will occupy at standard temperature and pressure (STP). To solve this problem, we use the combined gas law, which relates the pressure, volume, and temperature of a gas sample. The combined gas law is expressed as (P1 × V1) / T1 = (P2 × V2) / T2 where P represents pressure, V represents volume, and T represents temperature in Kelvin.
To find the volume at STP, we need to use the conditions given (40°C and 720 mmHg for the initial state and 0°C and 760 mmHg for the STP conditions). First, we convert the temperatures to Kelvin by adding 273.15 to the Celsius temperatures. So, 40°C becomes 313.15 K and 0°C becomes 273.15 K. Now we can solve for the unknown volume, V2.
To do that, rearrange the combined gas law to solve for V2: V2 = (P1 × V1 × T2) / (P2 × T1). Plugging in the values: V2 = (720 mmHg × 652 mL × 273.15 K) / (760 mmHg × 313.15 K). Calculating this gives us the volume of sulfur dioxide at STP.