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Difficulty: EasyBoyle's Law and Pressure-Volume Relationship

A sample of neon gas occupies a volume of 300 cm3300\text{ cm}^3 at a pressure of 100 kPa100\text{ kPa} under isothermal conditions. If the pressure on the gas is increased to 150 kPa150\text{ kPa}, what is the final volume of the gas?

  1. 200 cm3200\text{ cm}^3Answer
  2. B
    450 cm3450\text{ cm}^3
  3. C
    500 cm3500\text{ cm}^3
  4. D
    150 cm3150\text{ cm}^3

Answer

The final volume of the gas is 200 cm3200\text{ cm}^3.
According to Boyle's law, pressure and volume are inversely proportional at constant temperature (P1V1=P2V2P_1 V_1 = P_2 V_2). Multiplying the initial pressure (100 kPa100\text{ kPa}) by the initial volume (300 cm3300\text{ cm}^3) gives 30000 kPa⋅cm330000\text{ kPa}\cdot\text{cm}^3. Dividing this product by the final pressure (150 kPa150\text{ kPa}) yields the correct volume of 200 cm3200\text{ cm}^3.

Step-by-Step Solution

1
Identify the given parameters and constant conditions
P1=100 kPaP_1 = 100\text{ kPa}, V1=300 cm3V_1 = 300\text{ cm}^3, P2=150 kPaP_2 = 150\text{ kPa}, temperature is constant.
Boyle's law applies when mass and temperature are kept constant.
2
State Boyle's Law formula
P1V1=P2V2P_1 V_1 = P_2 V_2
Pressure and volume are inversely proportional for a fixed mass of gas at constant temperature.
3
Substitute the values into the formula and solve for the unknown volume (V2V_2)
V2=P1V1P2=100×300150=200 cm3V_2 = \frac{P_1 V_1}{P_2} = \frac{100 \times 300}{150} = 200\text{ cm}^3
Rearranging the equation yields the new volume following compression.

Key Concept

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

Boyle's Law and Pressure-Volume Relationship

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