A sample of gas in a 10.0-L container exerts a pressure of 565 mm Hg. Calculate the pressure exerted by thrvgas if he volume is changed to 15.0 L at constant temperature.
Ah, the gas is playing a game of "Expand and Pressure!" I see what they're up to. Well, to calculate the pressure exerted when the volume changes, we can use the infamous Boyle's Law. According to this law, pressure and volume are inversely proportional at constant temperature.
So, let's do some math magic. The initial pressure (P1) is 565 mm Hg, and the initial volume (V1) is 10.0 L. When the volume (V2) changes to 15.0 L, we need to find the new pressure (P2).
Using Boyle's Law, we can set up the equation:
P1 * V1 = P2 * V2
Now let's plug in the values:
565 mm Hg * 10.0 L = P2 * 15.0 L
Now, we can solve for P2:
5650 mm Hg * L = P2 * 15.0 L
Dividing both sides by 15.0 L, we get:
P2 = 5650 mm Hg / 15.0 L
So, the pressure exerted by the gas when the volume is changed to 15.0 L is approximately 376.67 mm Hg.
To calculate the pressure exerted by the gas when the volume is changed to 15.0 L at constant temperature, you can use Boyle's Law. Boyle's Law states that the pressure and volume of a gas are inversely proportional at constant temperature.
The formula for Boyle's Law is:
P1 * V1 = P2 * V2
Where:
P1 = Initial pressure
V1 = Initial volume
P2 = Final pressure (to be calculated)
V2 = Final volume
Given:
P1 = 565 mm Hg
V1 = 10.0 L
V2 = 15.0 L
Now, substitute the given values into the formula and solve for P2:
565 mm Hg * 10.0 L = P2 * 15.0 L
5650 mm Hg * L = P2 * 15.0 L
Divide both sides of the equation by 15.0 L:
5650 mm Hg = P2
So, the pressure exerted by the gas when the volume is changed to 15.0 L at constant temperature is 5650 mm Hg.
To solve this problem, you can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature. The equation for Boyle's Law is P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Given:
P1 = 565 mm Hg (initial pressure)
V1 = 10.0 L (initial volume)
V2 = 15.0 L (final volume)
To find the final pressure (P2), we can rearrange the equation as follows:
P2 = (P1 * V1) / V2
Plugging in the given values:
P2 = (565 mm Hg * 10.0 L) / 15.0 L
Now we can calculate the final pressure:
P2 = (5650 mm Hg * L) / 15.0 L
P2 = 376.67 mm Hg
Therefore, the pressure exerted by the gas when the volume is changed to 15.0 L at constant temperature is approximately 376.67 mm Hg.