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Boyle's Law states that for a fixed mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. Mathematically, this is expressed as P1 V1 = P2 V2.

Physics

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Answer

71.6 cm3\text{71.6 cm}^3

Step-by-step solution

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Here is the solution for question 2(b), which applies Boyle's Law.

Boyle's Law states that for a fixed mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. Mathematically, this is expressed as P1V1=P2V2P_1 V_1 = P_2 V_2.

  • Initial conditions:

    • Volume, V1=40 cm3V_1 = 40 \text{ cm}^3
    • Temperature, T1=0∘CT_1 = 0^\circ C
    • Pressure, P1=680 mmHgP_1 = 680 \text{ mmHg}
  • Final conditions for part (b):

    • Temperature, T2=0∘CT_2 = 0^\circ C (constant)
    • Pressure, P2=380 mmHgP_2 = 380 \text{ mmHg}
    • Volume, V2=?V_2 = ?
  1. Identify the given values.

    P1=680 mmHgP_1 = 680 \text{ mmHg} V1=40 cm3V_1 = 40 \text{ cm}^3 P2=380 mmHgP_2 = 380 \text{ mmHg}

    Since the temperature is constant (T1=T2=0∘CT_1 = T_2 = 0^\circ C), we can use Boyle's Law.

  2. Apply Boyle's Law formula.

    P1V1=P2V2P_1 V_1 = P_2 V_2
  3. Rearrange the formula to solve for V2V_2.

    V2=P1V1P2V_2 = \frac{P_1 V_1}{P_2}
  4. Substitute the values and calculate.

    V2=(680 mmHg)×(40 cm3)380 mmHgV_2 = \frac{(680 \text{ mmHg}) \times (40 \text{ cm}^3)}{380 \text{ mmHg}} V2=27200 cm3380V_2 = \frac{27200 \text{ cm}^3}{380} V2=71.5789... cm3V_2 = 71.5789... \text{ cm}^3
  5. Round the answer to an appropriate number of significant figures.

    V2≈71.6 cm3V_2 \approx 71.6 \text{ cm}^3

    The volume the gas would occupy at 0∘C0^\circ C and 380 mmHg380 \text{ mmHg} pressure is 71.6 cm3\boxed{\text{71.6 cm}^3}.

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