a gas has a volume of 410 mL at 27 degrees c and 740 mm Hg. what volume would this gas occupy at STP?
To find the volume of the gas at STP (Standard Temperature and Pressure), we need to first understand the conditions of STP. It is defined as a temperature of 0 degrees Celsius (0°C) or 273.15 Kelvin (K), and a pressure of 1 atmosphere (atm) or 760 millimeters of mercury (mmHg).
Given:
Initial volume (V1) = 410 mL
Initial temperature (T1) = 27°C
Initial pressure (P1) = 740 mmHg
To solve this problem, we can use the combined gas law, which states that the ratio of the initial pressure, volume, and temperature of a gas is equal to the ratio of the final pressure, volume, and temperature.
So, the combined gas law can be expressed as:
(P1 * V1) / T1 = (P2 * V2) / T2
Now, we can substitute the values we know:
(P1 * V1) / T1 = (P2 * V2) / T2
We want to find V2, the final volume at STP. Given that T2 is the temperature at STP (0°C or 273.15 K) and P2 is the pressure at STP (760 mmHg), we can rewrite the equation as:
(740 mmHg * 410 mL) / 27°C = (760 mmHg * V2) / 273.15 K
To convert Celsius to Kelvin, we add 273.15 to the temperature. So, 27°C = 27 + 273.15 = 300.15 K.
Now, we can rearrange the equation and solve for V2:
(740 mmHg * 410 mL * 273.15 K) / (27°C * 760 mmHg) = V2
Calculating this expression will give us the final volume (V2) of the gas at STP.