Questions: If the volume at a certain temperature is 40 mL and suddenly pressure is doubled, then the new volume will be a 20 mL b 30 mL c 40 mL d 80 mL

Solution Steps

The problem involves a gas at a certain temperature with an initial volume of 40 mL. The pressure is then doubled, and we need to find the new volume. This is a classic application of Boyle's Law, which states that for a given mass of gas at constant temperature, the pressure and volume are inversely proportional.

Boyle's Law is mathematically expressed as:

$$P_1 V_1 = P_2 V_2$$

where:

• $P_1$ and $V_1$ are the initial pressure and volume,
• $P_2$ and $V_2$ are the final pressure and volume.

Given that the initial volume $V_1 = 40$ mL and the pressure is doubled ($P_2 = 2P_1$), we can substitute these into the equation:

$$P_1 \times 40 = 2P_1 \times V_2$$

Cancel $P_1$ from both sides of the equation:

$$40 = 2 \times V_2$$

Now, solve for $V_2$:

$$V_2 = \frac{40}{2} = 20 \text{ mL}$$

Final Answer