a 2.50mL sample of dry air in a cylinder exerts a pressure of3.00atm at room temperature. without changing the temperature, a piston is moved until the pressure in the cylinder is reduced to 1.00atm. what is the final volume of the gas?
P1 times V1 =P2 times V2
As you increase pressure you decrease volume
As you decrease pressure you increase volume.
To solve this problem, we can use the combined gas law, which states that the product of pressure and volume divided by the temperature remains constant for a given amount of gas. The formula is as follows:
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 problem, the temperature remains constant, so T1 = T2. Therefore, we can simplify the equation to:
P1 * V1 = P2 * V2
Now let's plug in the given values:
P1 = 3.00 atm
V1 = 2.50 mL
P2 = 1.00 atm
V2 = ?
To find V2, we rearrange the equation and solve for it:
V2 = (P1 * V1) / P2
= (3.00 atm * 2.50 mL) / 1.00 atm
Calculating this gives:
V2 = 7.50 mL
Therefore, the final volume of the gas is 7.50 mL.