If the pressure of 20.0 mL of a gas sample is increased by 4 times and the absolute temperature is doubled, what is the new volume?
To find the new volume, we can use Boyle's Law and Charles's Law.
According to Boyle's Law, for a fixed amount of gas at constant temperature, the pressure and volume are inversely proportional. Mathematically, this can be represented as:
P1 * V1 = P2 * V2
where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
In this case, the initial volume is given as 20.0 mL, and the pressure is increased by 4 times. So, we can write:
P1 = 1
V1 = 20.0 mL
P2 = 4
V2 = ?
To find the new volume, we need to solve the equation:
1 * 20.0 mL = 4 * V2
By rearranging the equation, we can solve for V2:
V2 = (1 * 20.0 mL) / 4
V2 = 5.0 mL
So, the new volume after increasing the pressure by 4 times is 5.0 mL.
Now, let's consider Charles's Law, which states that for a fixed amount of gas at constant pressure, the volume is directly proportional to the absolute temperature. Mathematically, this can be represented as:
V1 / T1 = V2 / T2
where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.
In this case, the initial volume (V1) is 5.0 mL (as calculated earlier), and the absolute temperature is doubled. So, we can write:
V1 = 5.0 mL
T1 = 1 (let's assume a normalized temperature scale)
V2 = ?
T2 = 2
To find the new volume, we rearrange the equation and solve for V2:
V2 = (V1 * T2) / T1
V2 = (5.0 mL * 2) / 1
V2 = 10.0 mL
Therefore, after increasing the pressure by 4 times and doubling the absolute temperature, the new volume is 10.0 mL.