Question

A syringe has a volume of \(10.0 \text{cm}^3\) at a pressure of \(1\) atm. If the end is sealed and the plunger is pushed down (constant temperature), what will be the final volume when the pressure becomes \(3.5\) atm?

• A. \(35.0 \text{cm}^3\)
• B. \(2.86 \text{cm}^3\)
• C. \(0.286 \text{cm}^3\)
• D. \(3.50 \text{cm}^3\)

Hint:

Use Boyle's law, P1V1 = P2V2, because temperature is constant.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The syringe is sealed and the temperature is constant, so the amount of gas and temperature do not change. This is the situation described by Boyle's law.

Step 2: Key Formula:
\[ P_1V_1 = P_2V_2 \]

Step 3: Substitute the values:
\(P_1 = 1\) atm, \(V_1 = 10.0 \text{ cm}^3\), \(P_2 = 3.5\) atm.
\[ V_2 = \dfrac{P_1V_1}{P_2} = \dfrac{1 \times 10.0}{3.5} = 2.857 \text{ cm}^3 \approx 2.86 \text{ cm}^3 \]

Step 4: Why the other options are wrong.
35.0 cm\(^3\) multiplies the pressure by the volume instead of dividing, but pressure up must make volume go down. 0.286 cm\(^3\) is off by a factor of 10. 3.50 cm\(^3\) just reuses the pressure value and ignores the 10.0 cm\(^3\).

Final Answer:
The final volume is \(2.86 \text{ cm}^3\). \[ \boxed{\text{(B) }2.86\ \text{cm}^3} \]