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:

P1V1=P2V2 P_1 V_1 = P_2 V_2

where:

  • P1 P_1 and V1 V_1 are the initial pressure and volume,
  • P2 P_2 and V2 V_2 are the final pressure and volume.

Given that the initial volume V1=40 V_1 = 40 mL and the pressure is doubled (P2=2P1 P_2 = 2P_1 ), we can substitute these into the equation:

P1×40=2P1×V2 P_1 \times 40 = 2P_1 \times V_2

Step 3: Solve for the New Volume

Cancel P1 P_1 from both sides of the equation:

40=2×V2 40 = 2 \times V_2

Now, solve for V2 V_2 :

V2=402=20 mL V_2 = \frac{40}{2} = 20 \text{ mL}

Final Answer

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

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