STP (Standard Temperature and Pressure) is defined as 0 degrees Celsius (273.15 Kelvin) and 1 atmosphere of pressure (760 mmHg or 101.325 kPa). To calculate the volume of the gas at STP, we can use the combined gas law, which relates the initial and final conditions of pressure, volume, and temperature:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where: P1 = initial pressure V1 = initial volume T1 = initial temperature P2 = final pressure (STP) V2 = final volume at STP T2 = final temperature (STP)
Plugging in the values we know: P1 = 860 mmHg V1 = 400 mL T1 = 30 degrees Celsius (303.15 Kelvin) P2 = 760 mmHg T2 = 0 degrees Celsius (273.15 Kelvin)
Let's solve for V2:
(860 mmHg * 400 mL) / (303.15 K) = (760 mmHg * V2) / (273.15 K)
(860 * 400) / 303.15 = (760 * V2) / 273.15
V2 = (760 * (860 * 400) / (303.15 * 273.15)) mL
Calculating this equation gives us:
V2 ≈ 566.59 mL
Therefore, the gas would occupy approximately 566.59 mL at STP.