What volume does 627 cm3 of a gas at 14°C occupy at 40°C, if the pressure does not change?
To solve this problem, we can use the ideal gas law, which states that for a fixed amount of gas at constant pressure, the ratio of the initial volume to the final volume is equal to the ratio of the initial absolute temperature to the final absolute temperature.
The equation for the ideal gas law is:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = gas constant
T = temperature in Kelvin
First, we need to convert the given temperatures from Celsius to Kelvin. To convert Celsius to Kelvin, you add 273.15 to the Celsius value.
Given:
Initial volume (V1) = 627 cm^3
Initial temperature (T1) = 14°C = 14 + 273.15 = 287.15 K
Final temperature (T2) = 40°C = 40 + 273.15 = 313.15 K
Since the pressure remains constant, we can ignore the "P" term in the ideal gas law equation. Thus, we can rewrite the equation as:
V1 / V2 = T1 / T2
Now, plug in the given values:
627 cm^3 / V2 = 287.15 K / 313.15 K
To solve for V2 (final volume):
V2 = (627 cm^3) * (313.15 K) / (287.15 K)
Calculating this expression will give you the final volume (V2) in cm^3.
Therefore, to find the volume that 627 cm^3 of gas at 14°C occupies at 40°C, if the pressure does not change, you would use the equation V2 = (627 cm^3) * (313.15 K) / (287.15 K) and solve for V2.
(V1/T1) = (V2/T2)
Remember T must be in kelvin.