A sample of ideal gas at room temperature occupies a volume of 32.0L at a pressure of 272torr . If the pressure changes to 1360torr , with no change in the temperature or moles of gas, what is the new volume, V 2 ?
To find the new volume (V2) of the ideal gas, we can use the combined gas law equation, which states:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume (unknown)
T2 = final temperature (same as initial temperature)
Since the temperature and moles of gas remain constant, we can simplify the equation to:
(P1 * V1) = (P2 * V2)
Now we can substitute the given values:
P1 = 272 torr
V1 = 32.0 L
P2 = 1360 torr
Plug these values into the equation:
(272 torr * 32.0 L) = (1360 torr * V2)
8704 torr * L = 1360 torr * V2
To solve for V2, we can rearrange the equation:
V2 = (8704 torr * L) / 1360 torr
Now, divide 8704 torr * L by 1360 torr:
V2 ≈ 6.4 L
Therefore, the new volume (V2) is approximately 6.4 L when the pressure changes to 1360 torr with no change in temperature or moles of gas.
To find the new volume (V2) when the pressure changes, we can use Boyle's Law. According to Boyle's Law, the pressure and volume of a gas are inversely proportional when temperature and moles of gas remain constant.
The formula for Boyle's Law is:
P1 V1 = P2 V2
where P1 and V1 are the initial pressure and volume, respectively, and P2 and V2 are the final pressure and volume, respectively.
In this case, we are given the initial pressure (P1 = 272 torr), the initial volume (V1 = 32.0 L), and the final pressure (P2 = 1360 torr).
Plugging these values into the formula, we can solve for V2:
P1 V1 = P2 V2
(272 torr) (32.0 L) = (1360 torr) V2
Dividing both sides of the equation by 1360 torr to isolate V2, we have:
(272 torr) (32.0 L) / 1360 torr = V2
Simplifying the expression further, we get:
V2 ≈ 6.4 L
Therefore, the new volume (V2) is approximately 6.4 L when the pressure changes to 1360 torr with no change in temperature or moles of gas.