calculate the final volume of gas if the original pressure of gas at STP is doubled and its temperature is 3 times.
To calculate the final volume of gas, we can use the combined gas law, which relates the initial and final conditions of pressure, volume, and temperature. The formula for the combined gas law is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure of the gas
V1 = initial volume of the gas
T1 = initial temperature of the gas
P2 = final pressure of the gas
V2 = final volume of the gas (what we need to find)
T2 = final temperature of the gas
In this case, the gas is initially at Standard Temperature and Pressure (STP), which is defined as 1 atmosphere (atm) of pressure and 273 Kelvin (K) of temperature.
Let's assume that the initial volume of the gas at STP is V1. And we are given:
P1 = 1 atm
T1 = 273 K
P2 = 2 * P1 = 2 atm (since the original pressure is doubled)
T2 = 3 * T1 = 3 * 273 K (since the temperature is 3 times)
Now we can plug these values into the combined gas law formula and solve for V2:
(P1 * V1) / T1 = (P2 * V2) / T2
(1 atm * V1) / 273 K = (2 atm * V2) / (3 * 273 K)
Simplifying the equation:
(1 * V1) / 273 = (2 * V2) / (3 * 273)
V1 = (2 * V2) / 3
Multiplying both sides by 273:
273 * V1 = 2 * V2
Dividing by 2:
(273 * V1) / 2 = V2
Therefore, the final volume of the gas (V2) is (273 * V1) / 2.