To determine the volume of a gas at a different temperature using the ideal gas law, we need to assume that the pressure and the amount of gas (moles) remain constant. The ideal gas law equation is given as:
PV = nRT
Where: P is the pressure of the gas V is the volume of the gas n is the number of moles of the gas R is the ideal gas constant (8.314 J/(mol·K)) T is the temperature in Kelvin
To solve for the volume at a different temperature, we can rearrange the equation as follows:
V1/T1 = V2/T2
Where: V1 is the initial volume of the gas T1 is the initial temperature of the gas V2 is the volume of the gas at a different temperature T2 is the different temperature in Kelvin
Now let's calculate the volume of the gas at -23.0°C (-23.0°C + 273.15 = 250.15 K) using the given information:
V1 = 8.00 L T1 = 210.0°C (210.0°C + 273.15 = 483.15 K) T2 = -23.0°C (250.15 K)
Using the equation:
V1/T1 = V2/T2
8.00 L / 483.15 K = V2 / 250.15 K
Cross-multiplying, we get:
8.00 L * 250.15 K = V2 * 483.15 K
2001.2 = V2 * 483.15
Dividing both sides by 483.15:
V2 = 2001.2 / 483.15
V2 ≈ 4.14 L
Therefore, the volume of the gas at -23.0°C is approximately 4.14 L.