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

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
Transcript text: If the volume at a certain temperature is 40 mL and suddenly pressure is doubled, then the new volume will be $\qquad$ a 20 mL b $\quad 30 \mathrm{~mL}$ c 40 mL d 80 mL
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Solution

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Solution Steps

Step 1: Understand the Problem

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.

Step 2: Apply Boyle's Law

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:

\[ P_1 \times 40 = 2P_1 \times V_2 \]

Step 3: Solve for the New Volume

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

The new volume when the pressure is doubled is \(\boxed{20 \text{ mL}}\).

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