a sample of gas has a volume of 12liters at 0 degrees celcius and 380 torr. what will be its volume whent the pressure is changed to 760 torr at a constant temperature?
P1V1 = P2V2
To find the new volume of the gas when the pressure is changed, we can use the combined gas law. The combined gas law states that for a given amount of gas at a constant temperature, the ratio of the product of its pressure and volume is constant.
The formula for the combined gas law is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 and P2 are the initial and final pressures, respectively.
V1 and V2 are the initial and final volumes, respectively.
T1 and T2 are the initial and final temperatures, respectively.
In this case, we are given:
P1 = 380 torr (initial pressure)
V1 = 12 liters (initial volume)
P2 = 760 torr (final pressure)
T1 = 0 degrees Celsius (constant temperature)
Let's substitute these values into the combined gas law formula and solve for V2 (final volume):
(380 torr * 12 liters) / (0 degrees Celsius) = (760 torr * V2) / (0 degrees Celsius)
Next, cross-multiply and solve for V2:
(380 torr * 12 liters) * (0 degrees Celsius) = (760 torr) * (V2)
4,560 torr * liters = 760 torr * V2
Divide both sides by 760 torr to isolate V2:
V2 = (4,560 torr * liters) / (760 torr)
V2 ≈ 6 liters
Therefore, when the pressure is changed to 760 torr at a constant temperature, the volume of the gas will be approximately 6 liters.