an ideal gas at 75.0 c and 760 .mm hg is contained in a flexible vessel. Its volume is doubled and the pressure remains.unchanged .determine the temperature of the gas as a consequence of these changes
(V1/T1) = (V2/T2)
Don't forget T must be in Kelvin.
To determine the temperature of the gas as a consequence of these changes, we can use the ideal gas law:
PV = nRT
Where:
P = pressure (in this case, 760 mmHg)
V = volume (initial volume doubled)
n = number of moles of gas (constant)
R = ideal gas constant
T = temperature
In this case, we are told that the pressure remains unchanged and the volume is doubled. Therefore, we have:
P1V1 = P2V2
Since P1 = P2 and V1 is doubled, we can rewrite the equation as:
P1 * 2V1 = P1 * V2
Simplifying the equation, we find:
2V1 = V2
We know that the volume is doubled, so V2 = 2V1.
Now we can rearrange the ideal gas law equation and solve for temperature (T):
P1V1 / T1 = P2V2 / T2
Since P1 = P2 and V2 = 2V1, we have:
P1V1 / T1 = P1 * 2V1 / T2
We can cancel out P1 and V1:
1 / T1 = 2 / T2
Rearranging the equation, we find:
T2 = T1 / 2
Substituting the given temperature of 75.0 °C into the equation:
T2 = 75.0 °C / 2
T2 = 37.5 °C
Therefore, as a consequence of doubling the volume while keeping the pressure unchanged, the temperature of the gas would be 37.5 °C.