STP (Standard Temperature and Pressure) is defined as 0 degrees Celsius (273.15 Kelvin) and 1 atmosphere of pressure (760 mmHg). To find the volume of the gas at STP, we can use the combined gas law, which states that the ratio of the initial pressure, initial volume, and initial temperature of a gas to the final pressure, final volume, and final temperature of the gas is constant.
The combined gas law equation is as follows:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where: P1 = Initial pressure V1 = Initial volume T1 = Initial temperature (in Kelvin) P2 = Final pressure (STP) V2 = Final volume (to be found) T2 = Final temperature (in Kelvin, which is 273.15 K for STP)
Let's plug in the given values into the equation:
(800 mmHg * 480 ml) / (30 + 273.15 K) = (760 mmHg * V2) / (273.15 K)
Simplifying the equation:
(800 mmHg * 480 ml * 273.15 K) = (760 mmHg * V2 * (30 + 273.15 K))
Now, we can solve for V2:
V2 = (800 mmHg * 480 ml * 273.15 K) / (760 mmHg * (30 + 273.15 K))
Calculating the expression:
V2 ≈ 433.43 ml
Therefore, the volume of the gas at STP is approximately 433.43 ml.