charles law: 7.89 l sample of gas had pressure of 850 torr. what volume will it occupy if the pressure is changed to 457 torr? (torr is a measurement of pressure. 760 torr = 1 atmosphere
Looks more like Boyle's law to me.
P1V1 = P2V2
To solve this problem using Charles's law, we need to use the formula:
V1 / T1 = V2 / T2
Where:
V1 is the initial volume of the gas
T1 is the initial temperature of the gas
V2 is the final volume of the gas (what we are looking for)
T2 is the final temperature of the gas
Since the problem doesn't provide any information about temperature, we can assume it remains constant. Therefore, we can eliminate the temperature from the equation:
V1 / T1 = V2 / T2
V1 / T = V2 / T
V1 = (V2 * T) / T
V1 = V2
Now we can simplify the equation to solve for V2:
V1 = V2 * (T / T)
V2 = V1 * (T / T)
We are given the initial volume V1 as 7.89 L. We want to find V2 when the pressure changes from 850 torr to 457 torr.
Using the formula, we have:
V2 = V1 * (P2 / P1)
Substituting the given values:
V2 = 7.89 L * (457 torr / 850 torr)
Calculating this:
V2 = 7.89 L * 0.537
V2 ≈ 4.24 L
Therefore, the volume of the gas will be approximately 4.24 liters when the pressure changes from 850 torr to 457 torr.
To solve this problem, we can use Charles's Law, which states that for a given amount of gas at a constant pressure, the volume of the gas is directly proportional to its temperature.
In this case, we are given the initial volume, pressure, and are asked to calculate the final volume. We can use the following formula derived from Charles's Law:
V1 / T1 = V2 / T2
where:
V1 is the initial volume
T1 is the initial temperature
V2 is the final volume we want to find
T2 is the final temperature, which is assumed to be constant.
Since the problem does not mention any change in temperature, we can assume that T1 = T2. Therefore, the equation becomes:
V1 / T = V2 / T
Now, let's plug in the values given in the problem:
V1 = 7.89 L (initial volume)
P1 = 850 torr (initial pressure)
P2 = 457 torr (final pressure)
First, we need to convert the pressures to atmospheres because the equation is based on the ideal gas law, which uses atmospheres as the standard unit of pressure.
1 atmosphere = 760 torr
P1 = 850 torr / 760 torr/atm = 1.12 atm
P2 = 457 torr / 760 torr/atm = 0.6 atm
Now, we can rearrange the equation to solve for V2:
V2 = (V1 * P2) / P1
Plugging in the values:
V2 = (7.89 L * 0.6 atm) / 1.12 atm
V2 = 4.19 L
Therefore, the gas will occupy a volume of 4.19 liters if the pressure is changed to 457 torr.