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
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
Solution
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
where:
P1 and V1 are the initial pressure and volume,
P2 and V2 are the final pressure and volume.
Given that the initial volume V1=40 mL and the pressure is doubled (P2=2P1), we can substitute these into the equation:
P1×40=2P1×V2
Step 3: Solve for the New Volume
Cancel P1 from both sides of the equation:
40=2×V2
Now, solve for V2:
V2=240=20 mL
Final Answer
The new volume when the pressure is doubled is 20 mL.