STP (Standard Temperature and Pressure) is defined as a temperature of 0 degrees Celsius (273.15 Kelvin) and a pressure of 1 atmosphere (ATM). To calculate the volume of the gas at STP, we can use the combined gas law, which states:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where: P1 = Initial pressure V1 = Initial volume T1 = Initial temperature P2 = Final pressure (STP pressure, 1 ATM) V2 = Final volume (what we want to find) T2 = Final temperature (STP temperature, 273.15 K)
Using the given values: P1 = 0.9 ATM V1 = 200 cm³ T1 = 18°C = 18 + 273.15 = 291.15 K P2 = 1 ATM T2 = 0°C = 0 + 273.15 = 273.15 K
Plugging in the values into the equation:
(0.9 * 200) / 291.15 = (1 * V2) / 273.15
Solving for V2 (final volume):
V2 = (0.9 * 200 * 273.15) / (291.15)
V2 ≈ 168.84 cm³
Therefore, the volume of the gas at STP is approximately 168.84 cm³.