A gas is contained in a metal cylinder with a piston, so that the volume of the cylinder can change. If the gas initially occupies volume of 664 ml at 471 mmHg, what will be the volume if the temperature is kept constant and the pressure is changed to 408 mmHg?

To find the final volume of the gas when the pressure is changed, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when the temperature is kept constant.

Boyle's Law can be mathematically expressed as:

P1 * V1 = P2 * V2

Where P1 and V1 are the initial pressure and volume of the gas, and P2 and V2 are the final pressure and volume of the gas.

Given:
Initial volume, V1 = 664 ml
Initial pressure, P1 = 471 mmHg
Final pressure, P2 = 408 mmHg

Let's calculate the final volume, V2.

Using Boyle's Law equation:

P1 * V1 = P2 * V2

Rearranging the equation to solve for V2:

V2 = (P1 * V1) / P2

Plugging in the given values:

V2 = (471 mmHg * 664 ml) / 408 mmHg

Calculating the final volume:

V2 ≈ 765.1 ml

Therefore, when the pressure is changed to 408 mmHg while keeping the temperature constant, the volume of the gas will be approximately 765.1 ml.