A sample of gas at 80°C is cooled by 30 degrees until its final volume is 1.75 L. If the pressure remains constant, what was the initial volume of the gas.
To solve this problem, we can utilize the ideal gas law, which states that the product of pressure (P) and volume (V) is directly proportional to the product of the number of moles (n) and the absolute temperature (T) of a gas.
Mathematically, the equation is expressed as PV = nRT, where R is the gas constant. In this case, since the pressure remains constant, we can simplify the equation to V1/T1 = V2/T2, where V1 and T1 represent the initial volume and temperature, and V2 and T2 represent the final volume and temperature.
Given that the initial temperature (T1) is 80°C and it decreases by 30 degrees, we can calculate T1 and T2 as follows:
T1 = 80°C + 273.15
T2 = (80°C - 30°C) + 273.15
Converting the temperatures to Kelvin:
T1 = 353.15 K
T2 = 323.15 K
We are given the final volume (V2) as 1.75 L. Now we can substitute the values into the equation:
V1/T1 = V2/T2
V1 / 353.15 = 1.75 / 323.15
To isolate V1, we can cross multiply:
V1 = (1.75 x 353.15) / 323.15
V1 ≈ 1.910 L
Therefore, the initial volume of the gas is approximately 1.910 liters.
(V1/T1) = (V2/T2)
Remember T must be in kelvin.